LMFDB - Embedded newform 69.2.e.c.55.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,2,Mod(4,69)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("69.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	69.e (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.550967773947$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 7 x^{19} + 24 x^{18} - 70 x^{17} + 209 x^{16} - 527 x^{15} + 1115 x^{14} - 2187 x^{13} + \cdots + 529 $ x^20 - 7x^19 + 24x^18 - 70x^17 + 209x^16 - 527x^15 + 1115x^14 - 2187x^13 + 4165x^12 - 7040x^11 + 10649x^10 - 13519x^9 + 15111x^8 - 12101x^7 + 8244x^6 - 2837x^5 + 1859x^4 - 1730x^3 + 1957x^2 - 1656*x + 529
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			55.1
Root			$1.05639 - 1.21914i$ of defining polynomial
Character	$\chi$	$=$	69.55
Dual form			69.2.e.c.64.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.90549 + 0.559503i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(1.63535 - 1.05098i) q^{4} +(-0.291446 - 2.02705i) q^{5} +(1.67068 + 1.07368i) q^{6} +(1.34249 - 2.93963i) q^{7} +(0.0729013 - 0.0841325i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(-1.90549 + 0.559503i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(1.63535 - 1.05098i) q^{4} +(-0.291446 - 2.02705i) q^{5} +(1.67068 + 1.07368i) q^{6} +(1.34249 - 2.93963i) q^{7} +(0.0729013 - 0.0841325i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(1.68949 + 3.69946i) q^{10} +(-1.55951 - 0.457915i) q^{11} +(-1.86520 - 0.547672i) q^{12} +(-1.07824 - 2.36102i) q^{13} +(-0.913363 + 6.35258i) q^{14} +(-1.34109 + 1.54770i) q^{15} +(-1.70693 + 3.73765i) q^{16} +(3.90777 + 2.51137i) q^{17} +(-0.282628 - 1.96572i) q^{18} +(-5.38056 + 3.45787i) q^{19} +(-2.60700 - 3.00863i) q^{20} +(-3.10077 + 0.910468i) q^{21} +3.22785 q^{22} +(1.37375 - 4.59487i) q^{23} -0.111323 q^{24} +(0.773474 - 0.227113i) q^{25} +(3.37558 + 3.89563i) q^{26} +(0.841254 - 0.540641i) q^{27} +(-0.894050 - 6.21825i) q^{28} +(6.49822 + 4.17615i) q^{29} +(1.68949 - 3.69946i) q^{30} +(5.74006 - 6.62438i) q^{31} +(1.12962 - 7.85671i) q^{32} +(0.675196 + 1.47847i) q^{33} +(-8.85134 - 2.59899i) q^{34} +(-6.35005 - 1.86454i) q^{35} +(0.807544 + 1.76827i) q^{36} +(-1.13432 + 7.88940i) q^{37} +(8.31792 - 9.59939i) q^{38} +(-1.07824 + 2.36102i) q^{39} +(-0.191788 - 0.123254i) q^{40} +(0.407522 + 2.83438i) q^{41} +(5.39908 - 3.46978i) q^{42} +(2.44130 + 2.81741i) q^{43} +(-3.03161 + 0.890161i) q^{44} +2.04789 q^{45} +(-0.0468192 + 9.52410i) q^{46} -8.70030 q^{47} +(3.94253 - 1.15763i) q^{48} +(-2.25516 - 2.60259i) q^{49} +(-1.34678 + 0.865522i) q^{50} +(-0.661077 - 4.59789i) q^{51} +(-4.24468 - 2.72789i) q^{52} +(-0.624559 + 1.36759i) q^{53} +(-1.30051 + 1.50087i) q^{54} +(-0.473702 + 3.29467i) q^{55} +(-0.149450 - 0.327250i) q^{56} +(6.13680 + 1.80193i) q^{57} +(-14.7189 - 4.32185i) q^{58} +(2.08771 + 4.57145i) q^{59} +(-0.566554 + 3.94047i) q^{60} +(5.53965 - 6.39309i) q^{61} +(-7.23127 + 15.8343i) q^{62} +(2.71866 + 1.74718i) q^{63} +(1.07383 + 7.46864i) q^{64} +(-4.47166 + 2.87376i) q^{65} +(-2.11379 - 2.43945i) q^{66} +(-3.57857 + 1.05076i) q^{67} +9.02995 q^{68} +(-4.37218 + 1.97079i) q^{69} +13.1432 q^{70} +(1.18331 - 0.347451i) q^{71} +(0.0729013 + 0.0841325i) q^{72} +(9.93598 - 6.38547i) q^{73} +(-2.25270 - 15.6679i) q^{74} +(-0.678158 - 0.435826i) q^{75} +(-5.16495 + 11.3097i) q^{76} +(-3.43973 + 3.96966i) q^{77} +(0.733583 - 5.10218i) q^{78} +(3.73374 + 8.17574i) q^{79} +(8.07388 + 2.37071i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-2.36238 - 5.17288i) q^{82} +(2.18254 - 15.1799i) q^{83} +(-4.11396 + 4.74777i) q^{84} +(3.95177 - 8.65317i) q^{85} +(-6.22822 - 4.00264i) q^{86} +(-1.09930 - 7.64583i) q^{87} +(-0.152216 + 0.0978234i) q^{88} +(1.71060 + 1.97414i) q^{89} +(-3.90225 + 1.14580i) q^{90} -8.38806 q^{91} +(-2.58254 - 8.95799i) q^{92} -8.76531 q^{93} +(16.5784 - 4.86785i) q^{94} +(8.57742 + 9.89887i) q^{95} +(-6.67746 + 4.29134i) q^{96} +(-0.172893 - 1.20250i) q^{97} +(5.75334 + 3.69745i) q^{98} +(0.675196 - 1.47847i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 + 7 * q^6 - 6 * q^7 + 10 * q^8 - 2 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9} - 18 q^{10} - 16 q^{11} - 6 q^{12} + 14 q^{13} - 22 q^{14} + 5 q^{15} - 8 q^{16} + 11 q^{17} - 4 q^{18} - 11 q^{19} + 57 q^{20} - 6 q^{21} + 26 q^{22} - 12 q^{24} - 4 q^{25} - 14 q^{26} - 2 q^{27} - 14 q^{28} + 12 q^{29} - 18 q^{30} + 41 q^{31} - 46 q^{32} - 5 q^{33} - 3 q^{34} - 26 q^{35} + 5 q^{36} - 18 q^{37} + 70 q^{38} + 14 q^{39} - 13 q^{40} + 44 q^{42} - 10 q^{43} - 3 q^{44} + 16 q^{45} - 24 q^{46} + 18 q^{47} + 25 q^{48} - 10 q^{49} + 33 q^{50} + 61 q^{52} - 20 q^{53} + 7 q^{54} - 17 q^{55} + 6 q^{56} + 11 q^{57} - 37 q^{58} + 40 q^{59} - 31 q^{60} - 12 q^{61} - 89 q^{62} - 6 q^{63} - 2 q^{64} - 51 q^{65} + 15 q^{66} - 47 q^{67} - 12 q^{68} - 22 q^{69} + 32 q^{70} - 47 q^{71} + 10 q^{72} + 39 q^{73} - 50 q^{74} - 26 q^{75} - 39 q^{76} + 22 q^{77} - 14 q^{78} - 2 q^{79} + 12 q^{80} - 2 q^{81} + 26 q^{82} - 52 q^{83} - 14 q^{84} + 35 q^{85} + 34 q^{86} - 32 q^{87} + 30 q^{88} + 36 q^{89} - 18 q^{90} + 8 q^{91} - 19 q^{92} - 14 q^{93} + 21 q^{94} + 89 q^{95} - 2 q^{96} + 85 q^{98} - 5 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 + 7 * q^6 - 6 * q^7 + 10 * q^8 - 2 * q^9 - 18 * q^10 - 16 * q^11 - 6 * q^12 + 14 * q^13 - 22 * q^14 + 5 * q^15 - 8 * q^16 + 11 * q^17 - 4 * q^18 - 11 * q^19 + 57 * q^20 - 6 * q^21 + 26 * q^22 - 12 * q^24 - 4 * q^25 - 14 * q^26 - 2 * q^27 - 14 * q^28 + 12 * q^29 - 18 * q^30 + 41 * q^31 - 46 * q^32 - 5 * q^33 - 3 * q^34 - 26 * q^35 + 5 * q^36 - 18 * q^37 + 70 * q^38 + 14 * q^39 - 13 * q^40 + 44 * q^42 - 10 * q^43 - 3 * q^44 + 16 * q^45 - 24 * q^46 + 18 * q^47 + 25 * q^48 - 10 * q^49 + 33 * q^50 + 61 * q^52 - 20 * q^53 + 7 * q^54 - 17 * q^55 + 6 * q^56 + 11 * q^57 - 37 * q^58 + 40 * q^59 - 31 * q^60 - 12 * q^61 - 89 * q^62 - 6 * q^63 - 2 * q^64 - 51 * q^65 + 15 * q^66 - 47 * q^67 - 12 * q^68 - 22 * q^69 + 32 * q^70 - 47 * q^71 + 10 * q^72 + 39 * q^73 - 50 * q^74 - 26 * q^75 - 39 * q^76 + 22 * q^77 - 14 * q^78 - 2 * q^79 + 12 * q^80 - 2 * q^81 + 26 * q^82 - 52 * q^83 - 14 * q^84 + 35 * q^85 + 34 * q^86 - 32 * q^87 + 30 * q^88 + 36 * q^89 - 18 * q^90 + 8 * q^91 - 19 * q^92 - 14 * q^93 + 21 * q^94 + 89 * q^95 - 2 * q^96 + 85 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.90549	+	0.559503i	−1.34739	+	0.395628i	−0.874299	−	0.485387i	$-0.838679\pi$
$2$	−1.90549	+	0.559503i	−1.34739	+	0.395628i	−0.473087	+	0.881016i	$0.656860\pi$
$3$	−0.654861	−	0.755750i	−0.378084	−	0.436332i
$3$	−0.654861	−	0.755750i	−0.378084	−	0.436332i
$4$	1.63535	−	1.05098i	0.817675	−	0.525488i
$5$	−0.291446	−	2.02705i	−0.130339	−	0.906524i	−0.945112	−	0.326745i	$-0.894048\pi$
$5$	−0.291446	−	2.02705i	−0.130339	−	0.906524i	0.814774	−	0.579779i	$-0.196861\pi$
$6$	1.67068	+	1.07368i	0.682051	+	0.438327i
$7$	1.34249	−	2.93963i	0.507412	−	1.11108i	−0.466577	−	0.884481i	$-0.654513\pi$
$7$	1.34249	−	2.93963i	0.507412	−	1.11108i	0.973989	−	0.226597i	$-0.0727599\pi$
$8$	0.0729013	−	0.0841325i	0.0257745	−	0.0297453i
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$	1.68949	+	3.69946i	0.534263	+	1.16987i
$11$	−1.55951	−	0.457915i	−0.470211	−	0.138067i	0.0380383	−	0.999276i	$-0.487889\pi$
$11$	−1.55951	−	0.457915i	−0.470211	−	0.138067i	−0.508250	+	0.861210i	$0.669707\pi$
$12$	−1.86520	−	0.547672i	−0.538437	−	0.158099i
$13$	−1.07824	−	2.36102i	−0.299050	−	0.654829i	0.699138	−	0.714986i	$-0.253567\pi$
$13$	−1.07824	−	2.36102i	−0.299050	−	0.654829i	−0.998189	+	0.0601571i	$0.980840\pi$
$14$	−0.913363	+	6.35258i	−0.244106	+	1.69780i
$15$	−1.34109	+	1.54770i	−0.346267	+	0.399613i
$16$	−1.70693	+	3.73765i	−0.426732	+	0.934413i
$17$	3.90777	+	2.51137i	0.947773	+	0.609097i	0.920589	−	0.390534i	$-0.127710\pi$
$17$	3.90777	+	2.51137i	0.947773	+	0.609097i	0.0271842	+	0.999630i	$0.491346\pi$
$18$	−0.282628	−	1.96572i	−0.0666161	−	0.463325i
$19$	−5.38056	+	3.45787i	−1.23438	+	0.793290i	−0.984568	−	0.175003i	$-0.944007\pi$
$19$	−5.38056	+	3.45787i	−1.23438	+	0.793290i	−0.249816	+	0.968293i	$0.580370\pi$
$20$	−2.60700	−	3.00863i	−0.582942	−	0.672751i
$21$	−3.10077	+	0.910468i	−0.676643	+	0.198680i
$22$	3.22785			0.688180
$23$	1.37375	−	4.59487i	0.286446	−	0.958096i
$23$	1.37375	−	4.59487i	0.286446	−	0.958096i
$24$	−0.111323			−0.0227238
$25$	0.773474	−	0.227113i	0.154695	−	0.0454225i
$26$	3.37558	+	3.89563i	0.662006	+	0.763995i
$27$	0.841254	−	0.540641i	0.161899	−	0.104046i
$28$	−0.894050	−	6.21825i	−0.168960	−	1.17514i
$29$	6.49822	+	4.17615i	1.20669	+	0.775492i	0.980101	−	0.198498i	$-0.0636064\pi$
$29$	6.49822	+	4.17615i	1.20669	+	0.775492i	0.226588	+	0.973991i	$0.427243\pi$
$30$	1.68949	−	3.69946i	0.308457	−	0.675426i
$31$	5.74006	−	6.62438i	1.03094	−	1.18977i	0.0493530	−	0.998781i	$-0.484284\pi$
$31$	5.74006	−	6.62438i	1.03094	−	1.18977i	0.981592	−	0.190992i	$-0.0611705\pi$
$32$	1.12962	−	7.85671i	0.199691	−	1.38888i
$33$	0.675196	+	1.47847i	0.117537	+	0.257369i
$34$	−8.85134	−	2.59899i	−1.51799	−	0.445723i
$35$	−6.35005	−	1.86454i	−1.07335	−	0.315165i
$36$	0.807544	+	1.76827i	0.134591	+	0.294712i
$37$	−1.13432	+	7.88940i	−0.186482	+	1.29701i	0.654548	+	0.756021i	$0.272859\pi$
$37$	−1.13432	+	7.88940i	−0.186482	+	1.29701i	−0.841030	+	0.540989i	$0.818050\pi$
$38$	8.31792	−	9.59939i	1.34934	−	1.55723i
$39$	−1.07824	+	2.36102i	−0.172657	+	0.378066i
$40$	−0.191788	−	0.123254i	−0.0303243	−	0.0194882i
$41$	0.407522	+	2.83438i	0.0636443	+	0.442656i	0.996581	+	0.0826165i	$0.0263277\pi$
$41$	0.407522	+	2.83438i	0.0636443	+	0.442656i	−0.932937	+	0.360039i	$0.882763\pi$
$42$	5.39908	−	3.46978i	0.833096	−	0.535399i
$43$	2.44130	+	2.81741i	0.372295	+	0.429651i	0.910721	−	0.413022i	$-0.135527\pi$
$43$	2.44130	+	2.81741i	0.372295	+	0.429651i	−0.538427	+	0.842672i	$0.680981\pi$
$44$	−3.03161	+	0.890161i	−0.457032	+	0.134197i
$45$	2.04789			0.305282
$46$	−0.0468192	+	9.52410i	−0.00690312	+	1.40425i
$47$	−8.70030			−1.26907			−0.634535	−	0.772894i	$-0.718808\pi$
$47$	−8.70030			−1.26907			−0.634535	+	0.772894i	$0.718808\pi$
$48$	3.94253	−	1.15763i	0.569055	−	0.167090i
$49$	−2.25516	−	2.60259i	−0.322166	−	0.371799i
$50$	−1.34678	+	0.865522i	−0.190463	+	0.122403i
$51$	−0.661077	−	4.59789i	−0.0925693	−	0.643833i
$52$	−4.24468	−	2.72789i	−0.588631	−	0.378290i
$53$	−0.624559	+	1.36759i	−0.0857898	+	0.187853i	−0.947665	−	0.319268i	$-0.896563\pi$
$53$	−0.624559	+	1.36759i	−0.0857898	+	0.187853i	0.861875	+	0.507121i	$0.169290\pi$
$54$	−1.30051	+	1.50087i	−0.176977	+	0.204243i
$55$	−0.473702	+	3.29467i	−0.0638740	+	0.444253i
$56$	−0.149450	−	0.327250i	−0.0199711	−	0.0437306i
$57$	6.13680	+	1.80193i	0.812839	+	0.238671i
$58$	−14.7189	−	4.32185i	−1.93268	−	0.567487i
$59$	2.08771	+	4.57145i	0.271797	+	0.595152i	0.995479	−	0.0949816i	$-0.0302792\pi$
$59$	2.08771	+	4.57145i	0.271797	+	0.595152i	−0.723682	+	0.690133i	$0.757552\pi$
$60$	−0.566554	+	3.94047i	−0.0731418	+	0.508713i
$61$	5.53965	−	6.39309i	0.709279	−	0.818552i	−0.280696	−	0.959797i	$-0.590565\pi$
$61$	5.53965	−	6.39309i	0.709279	−	0.818552i	0.989975	+	0.141245i	$0.0451106\pi$
$62$	−7.23127	+	15.8343i	−0.918373	+	2.01096i
$63$	2.71866	+	1.74718i	0.342519	+	0.220123i
$64$	1.07383	+	7.46864i	0.134229	+	0.933580i
$65$	−4.47166	+	2.87376i	−0.554641	+	0.356446i
$66$	−2.11379	−	2.43945i	−0.260190	−	0.300275i
$67$	−3.57857	+	1.05076i	−0.437191	+	0.128371i	−0.492919	−	0.870075i	$-0.664070\pi$
$67$	−3.57857	+	1.05076i	−0.437191	+	0.128371i	0.0557280	+	0.998446i	$0.482252\pi$
$68$	9.02995			1.09504
$69$	−4.37218	+	1.97079i	−0.526349	+	0.237255i
$70$	13.1432			1.57091
$71$	1.18331	−	0.347451i	0.140433	−	0.0412349i	−0.210761	−	0.977538i	$-0.567594\pi$
$71$	1.18331	−	0.347451i	0.140433	−	0.0412349i	0.351194	+	0.936303i	$0.385776\pi$
$72$	0.0729013	+	0.0841325i	0.00859149	+	0.00991511i
$73$	9.93598	−	6.38547i	1.16292	−	0.747363i	0.190749	−	0.981639i	$-0.438908\pi$
$73$	9.93598	−	6.38547i	1.16292	−	0.747363i	0.972170	+	0.234276i	$0.0752721\pi$
$74$	−2.25270	−	15.6679i	−0.261871	−	1.82135i
$75$	−0.678158	−	0.435826i	−0.0783070	−	0.0503248i
$76$	−5.16495	+	11.3097i	−0.592460	+	1.29731i
$77$	−3.43973	+	3.96966i	−0.391994	+	0.452385i
$78$	0.733583	−	5.10218i	0.0830620	−	0.577709i
$79$	3.73374	+	8.17574i	0.420078	+	0.919843i	0.994834	+	0.101518i	$0.0323699\pi$
$79$	3.73374	+	8.17574i	0.420078	+	0.919843i	−0.574755	+	0.818325i	$0.694903\pi$
$80$	8.07388	+	2.37071i	0.902687	+	0.265053i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	−2.36238	−	5.17288i	−0.260881	−	0.571249i
$83$	2.18254	−	15.1799i	0.239565	−	1.66621i	−0.414710	−	0.909954i	$-0.636117\pi$
$83$	2.18254	−	15.1799i	0.239565	−	1.66621i	0.654275	−	0.756257i	$-0.272974\pi$
$84$	−4.11396	+	4.74777i	−0.448870	+	0.518024i
$85$	3.95177	−	8.65317i	0.428630	−	0.938568i
$86$	−6.22822	−	4.00264i	−0.671607	−	0.431615i
$87$	−1.09930	−	7.64583i	−0.117858	−	0.819719i
$88$	−0.152216	+	0.0978234i	−0.0162263	+	0.0104280i
$89$	1.71060	+	1.97414i	0.181323	+	0.209258i	0.839134	−	0.543925i	$-0.183063\pi$
$89$	1.71060	+	1.97414i	0.181323	+	0.209258i	−0.657810	+	0.753184i	$0.728517\pi$
$90$	−3.90225	+	1.14580i	−0.411333	+	0.120778i
$91$	−8.38806			−0.879308
$92$	−2.58254	−	8.95799i	−0.269248	−	0.933935i
$93$	−8.76531			−0.908920
$94$	16.5784	−	4.86785i	1.70993	−	0.502080i
$95$	8.57742	+	9.89887i	0.880025	+	1.01560i
$96$	−6.67746	+	4.29134i	−0.681515	+	0.437983i
$97$	−0.172893	−	1.20250i	−0.0175546	−	0.122095i	0.979160	−	0.203091i	$-0.0650989\pi$
$97$	−0.172893	−	1.20250i	−0.0175546	−	0.122095i	−0.996714	+	0.0809964i	$0.974190\pi$
$98$	5.75334	+	3.69745i	0.581176	+	0.373499i
$99$	0.675196	−	1.47847i	0.0678598	−	0.148592i
$100$	1.02621	−	1.18431i	0.102621	−	0.118431i
$101$	−1.08352	+	7.53601i	−0.107814	+	0.749861i	0.862157	+	0.506641i	$0.169113\pi$
$101$	−1.08352	+	7.53601i	−0.107814	+	0.749861i	−0.969971	+	0.243221i	$0.921796\pi$
$102$	3.83221	+	8.39137i	0.379445	+	0.830869i
$103$	−10.4040	−	3.05489i	−1.02514	−	0.301007i	−0.274405	−	0.961614i	$-0.588481\pi$
$103$	−10.4040	−	3.05489i	−1.02514	−	0.301007i	−0.750732	+	0.660607i	$0.770299\pi$
$104$	−0.277244	−	0.0814061i	−0.0271860	−	0.00798253i
$105$	2.74927	+	6.02006i	0.268301	+	0.587498i
$106$	0.424920	−	2.95538i	0.0412719	−	0.287052i
$107$	−3.00774	+	3.47111i	−0.290769	+	0.335565i	−0.882274	−	0.470736i	$-0.843988\pi$
$107$	−3.00774	+	3.47111i	−0.290769	+	0.335565i	0.591505	+	0.806301i	$0.298534\pi$
$108$	0.807544	−	1.76827i	0.0777059	−	0.170152i
$109$	0.710274	+	0.456465i	0.0680319	+	0.0437215i	0.574215	−	0.818705i	$-0.305307\pi$
$109$	0.710274	+	0.456465i	0.0680319	+	0.0437215i	−0.506183	+	0.862426i	$0.668944\pi$
$110$	−0.940743	−	6.54301i	−0.0896963	−	0.623851i
$111$	6.70524	−	4.30919i	0.636433	−	0.409011i
$112$	8.69580	+	10.0355i	0.821676	+	0.948264i
$113$	−10.6802	+	3.13598i	−1.00471	+	0.295009i	−0.742386	−	0.669972i	$-0.766306\pi$
$113$	−10.6802	+	3.13598i	−1.00471	+	0.295009i	−0.262321	+	0.964981i	$0.584488\pi$
$114$	−12.7018			−1.18963
$115$	−9.71440	−	1.44550i	−0.905873	−	0.134793i
$116$	15.0159			1.39419
$117$	2.49044	−	0.731259i	0.230241	−	0.0676049i
$118$	−6.53585	−	7.54278i	−0.601674	−	0.694369i
$119$	12.6286	−	8.11593i	1.15766	−	0.743986i
$120$	0.0324447	+	0.225658i	0.00296178	+	0.0205997i
$121$	−7.03139	−	4.51880i	−0.639217	−	0.410800i
$122$	−6.97880	+	15.2814i	−0.631831	+	1.38352i
$123$	1.87521	−	2.16411i	0.169082	−	0.195131i
$124$	2.42494	−	16.8658i	0.217766	−	1.51460i
$125$	−4.93942	−	10.8158i	−0.441796	−	0.967397i
$126$	−6.15793	−	1.80813i	−0.548592	−	0.161081i
$127$	17.4791	+	5.13231i	1.55102	+	0.455419i	0.941404	−	0.337281i	$-0.109507\pi$
$127$	17.4791	+	5.13231i	1.55102	+	0.455419i	0.609611	+	0.792700i	$0.291325\pi$
$128$	0.369818	+	0.809788i	0.0326876	+	0.0715758i
$129$	0.530545	−	3.69002i	0.0467119	−	0.324888i
$130$	6.91283	−	7.97783i	0.606295	−	0.699702i
$131$	0.603367	−	1.32119i	0.0527164	−	0.115433i	−0.881441	−	0.472294i	$-0.843426\pi$
$131$	0.603367	−	1.32119i	0.0527164	−	0.115433i	0.934157	+	0.356862i	$0.116153\pi$
$132$	2.65802	+	1.70821i	0.231351	+	0.148680i
$133$	2.94156	+	20.4590i	0.255066	+	1.77402i
$134$	6.23102	−	4.00444i	0.538279	−	0.345931i
$135$	−1.34109	−	1.54770i	−0.115422	−	0.133204i
$136$	0.496169	−	0.145688i	0.0425461	−	0.0124927i
$137$	−4.47536			−0.382356			−0.191178	−	0.981555i	$-0.561231\pi$
$137$	−4.47536			−0.382356			−0.191178	+	0.981555i	$0.561231\pi$
$138$	7.22850	−	6.20158i	0.615330	−	0.527913i
$139$	5.81596			0.493303			0.246652	−	0.969104i	$-0.420670\pi$
$139$	5.81596			0.493303			0.246652	+	0.969104i	$0.420670\pi$
$140$	−12.3441	+	3.62457i	−1.04327	+	0.306332i
$141$	5.69749	+	6.57525i	0.479815	+	0.553736i
$142$	−2.06039	+	1.32413i	−0.172904	+	0.111119i
$143$	0.600388	+	4.17579i	0.0502070	+	0.349197i
$144$	−3.45669	−	2.22148i	−0.288057	−	0.185123i
$145$	6.57139	−	14.3893i	0.545724	−	1.19497i
$146$	−15.3602	+	17.7267i	−1.27122	+	1.46707i
$147$	−0.490093	+	3.40867i	−0.0404222	+	0.281142i
$148$	6.43655	+	14.0941i	0.529081	+	1.15853i
$149$	0.0318508	+	0.00935225i	0.00260932	+	0.000766166i	0.283037	−	0.959109i	$-0.408658\pi$
$149$	0.0318508	+	0.00935225i	0.00260932	+	0.000766166i	−0.280428	+	0.959875i	$0.590476\pi$
$150$	1.53607	+	0.451031i	0.125420	+	0.0368265i
$151$	6.25711	+	13.7012i	0.509197	+	1.11499i	0.973370	+	0.229241i	$0.0736243\pi$
$151$	6.25711	+	13.7012i	0.509197	+	1.11499i	−0.464173	+	0.885745i	$0.653648\pi$
$152$	−0.101330	+	0.704763i	−0.00821892	+	0.0571638i
$153$	−3.04194	+	3.51059i	−0.245926	+	0.283814i
$154$	4.33334	−	9.48870i	0.349191	−	0.764621i
$155$	−15.1009	−	9.70473i	−1.21293	−	0.779503i
$156$	0.718072	+	4.99430i	0.0574918	+	0.399864i
$157$	−13.1292	+	8.43760i	−1.04782	+	0.673394i	−0.946909	−	0.321502i	$-0.895812\pi$
$157$	−13.1292	+	8.43760i	−1.04782	+	0.673394i	−0.100912	+	0.994895i	$0.532176\pi$
$158$	−11.6890	−	13.4898i	−0.929924	−	1.07319i
$159$	1.44256	−	0.423573i	0.114402	−	0.0335915i
$160$	−16.2552			−1.28508
$161$	−11.6630	−	10.2069i	−0.919173	−	0.804413i
$162$	1.98594			0.156030
$163$	−13.2652	+	3.89500i	−1.03901	+	0.305080i	−0.756368	−	0.654146i	$-0.773028\pi$
$163$	−13.2652	+	3.89500i	−1.03901	+	0.305080i	−0.282640	+	0.959226i	$0.591210\pi$
$164$	3.64531	+	4.20691i	0.284651	+	0.328504i
$165$	2.80016	−	1.79955i	0.217992	−	0.140095i
$166$	4.33439	+	30.1463i	0.336414	+	2.33981i
$167$	2.18969	+	1.40723i	0.169443	+	0.108895i	0.622614	−	0.782529i	$-0.286071\pi$
$167$	2.18969	+	1.40723i	0.169443	+	0.108895i	−0.453170	+	0.891424i	$0.649707\pi$
$168$	−0.149450	+	0.327250i	−0.0115303	+	0.0252479i
$169$	4.10138	−	4.73324i	0.315491	−	0.364096i
$170$	−2.68859	+	18.6996i	−0.206206	+	1.43419i
$171$	−2.65694	−	5.81790i	−0.203182	−	0.444906i
$172$	6.95341	+	2.04170i	0.530192	+	0.155678i
$173$	15.6378	+	4.59168i	1.18892	+	0.349099i	0.815607	−	0.578606i	$-0.196403\pi$
$173$	15.6378	+	4.59168i	1.18892	+	0.349099i	0.373314	+	0.927705i	$0.378221\pi$
$174$	6.37258	+	13.9540i	0.483104	+	1.05785i
$175$	0.370751	−	2.57863i	0.0280261	−	0.194926i
$176$	4.37350	−	5.04729i	0.329665	−	0.380454i
$177$	2.08771	−	4.57145i	0.156922	−	0.343611i
$178$	−4.36407	−	2.80462i	−0.327101	−	0.210215i
$179$	0.816896	+	5.68163i	0.0610576	+	0.424665i	0.997308	+	0.0733308i	$0.0233629\pi$
$179$	0.816896	+	5.68163i	0.0610576	+	0.424665i	−0.936250	+	0.351334i	$0.885728\pi$
$180$	3.34902	−	2.15229i	0.249622	−	0.160422i
$181$	−7.62337	−	8.79784i	−0.566641	−	0.653938i	0.398037	−	0.917369i	$-0.369691\pi$
$181$	−7.62337	−	8.79784i	−0.566641	−	0.653938i	−0.964678	+	0.263431i	$0.915146\pi$
$182$	15.9834	−	4.69315i	1.18477	−	0.347879i
$183$	−8.45927			−0.625327
$184$	−0.286430	−	0.450548i	−0.0211159	−	0.0332149i
$185$	16.3228			1.20008
$186$	16.7022	−	4.90422i	1.22467	−	0.359595i
$187$	−4.94423	−	5.70594i	−0.361558	−	0.417260i
$188$	−14.2280	+	9.14381i	−1.03769	+	0.666881i
$189$	−0.459915	−	3.19878i	−0.0334539	−	0.232677i
$190$	−21.8827	−	14.0631i	−1.58753	−	1.02025i
$191$	1.34149	−	2.93746i	0.0970670	−	0.212547i	−0.854869	−	0.518844i	$-0.826363\pi$
$191$	1.34149	−	2.93746i	0.0970670	−	0.212547i	0.951936	+	0.306297i	$0.0990899\pi$
$192$	4.94122	−	5.70247i	0.356602	−	0.411540i
$193$	−0.621799	+	4.32471i	−0.0447581	+	0.311299i	0.955128	+	0.296194i	$0.0957175\pi$
$193$	−0.621799	+	4.32471i	−0.0447581	+	0.311299i	−0.999886	+	0.0151054i	$0.995192\pi$
$194$	1.00225	+	2.19462i	0.0719572	+	0.157564i
$195$	5.10015	+	1.49754i	0.365230	+	0.107241i
$196$	−6.42323	−	1.88603i	−0.458802	−	0.134717i
$197$	−8.92138	−	19.5351i	−0.635622	−	1.39182i	−0.903594	−	0.428391i	$-0.859081\pi$
$197$	−8.92138	−	19.5351i	−0.635622	−	1.39182i	0.267972	−	0.963427i	$-0.413647\pi$
$198$	−0.459371	+	3.19499i	−0.0326461	+	0.227058i
$199$	−4.15479	+	4.79488i	−0.294525	+	0.339900i	−0.883655	−	0.468138i	$-0.844925\pi$
$199$	−4.15479	+	4.79488i	−0.294525	+	0.339900i	0.589130	+	0.808038i	$0.299470\pi$
$200$	0.0372797	−	0.0816311i	0.00263607	−	0.00577219i
$201$	3.13757	+	2.01640i	0.221307	+	0.142226i
$202$	−2.15179	−	14.9660i	−0.151400	−	1.05301i
$203$	21.0001	−	13.4960i	1.47392	−	0.947231i
$204$	−5.91336	−	6.82438i	−0.414018	−	0.477802i
$205$	5.62666	−	1.65214i	0.392983	−	0.115390i
$206$	21.5340			1.50034
$207$	4.35260	+	2.01368i	0.302526	+	0.139961i
$208$	10.6651			0.739495
$209$	9.97447	−	2.92877i	0.689948	−	0.202587i
$210$	−8.60696	−	9.93296i	−0.593936	−	0.685439i
$211$	−12.4219	+	7.98305i	−0.855157	+	0.549576i	−0.893179	−	0.449701i	$-0.851530\pi$
$211$	−12.4219	+	7.98305i	−0.855157	+	0.549576i	0.0380226	+	0.999277i	$0.487894\pi$
$212$	0.415935	+	2.89289i	0.0285665	+	0.198685i
$213$	−1.03749	−	0.666754i	−0.0710876	−	0.0456853i
$214$	3.78912	−	8.29702i	0.259019	−	0.567173i
$215$	4.99952	−	5.76976i	0.340965	−	0.393494i
$216$	0.0158430	−	0.110190i	0.00107798	−	0.00749749i
$217$	−11.7673	−	25.7668i	−0.798817	−	1.74916i
$218$	−1.60882	−	0.472391i	−0.108963	−	0.0319943i
$219$	−11.3325	−	3.32752i	−0.765779	−	0.224853i
$220$	2.68795	+	5.88579i	0.181222	+	0.396820i
$221$	1.71588	−	11.9342i	0.115422	−	0.802780i
$222$	−10.3658	+	11.9627i	−0.695705	+	0.802886i
$223$	−8.03655	+	17.5976i	−0.538167	+	1.17842i	0.423925	+	0.905697i	$0.360652\pi$
$223$	−8.03655	+	17.5976i	−0.538167	+	1.17842i	−0.962092	+	0.272725i	$0.912075\pi$
$224$	−21.5794	−	13.8682i	−1.44183	−	0.926609i
$225$	0.114724	+	0.797923i	0.00764827	+	0.0531949i
$226$	18.5964	−	11.9512i	1.23701	−	0.794981i
$227$	6.36225	+	7.34243i	0.422277	+	0.487334i	0.926529	−	0.376222i	$-0.122777\pi$
$227$	6.36225	+	7.34243i	0.422277	+	0.487334i	−0.504252	+	0.863557i	$0.668232\pi$
$228$	11.9296	−	3.50285i	0.790057	−	0.231982i
$229$	5.31591			0.351285			0.175642	−	0.984454i	$-0.443800\pi$
$229$	5.31591			0.351285			0.175642	+	0.984454i	$0.443800\pi$
$230$	19.3195	−	2.68085i	1.27389	−	0.176770i
$231$	5.25261			0.345597
$232$	0.825079	−	0.242265i	0.0541691	−	0.0159055i
$233$	11.0328	+	12.7325i	0.722781	+	0.834133i	0.991639	−	0.129046i	$-0.0411916\pi$
$233$	11.0328	+	12.7325i	0.722781	+	0.834133i	−0.268858	+	0.963180i	$0.586646\pi$
$234$	−4.33637	+	2.78682i	−0.283477	+	0.182180i
$235$	2.53567	+	17.6359i	0.165409	+	1.15044i
$236$	8.21861	+	5.28178i	0.534986	+	0.343815i
$237$	3.73374	−	8.17574i	0.242532	−	0.531072i
$238$	−19.5229	+	22.5306i	−1.26548	+	1.46044i
$239$	−2.02812	+	14.1059i	−0.131188	+	0.912433i	0.812821	+	0.582513i	$0.197931\pi$
$239$	−2.02812	+	14.1059i	−0.131188	+	0.912433i	−0.944009	+	0.329919i	$0.892978\pi$
$240$	−3.49561	−	7.65431i	−0.225640	−	0.494084i
$241$	−25.8093	−	7.57831i	−1.66253	−	0.488162i	−0.690558	−	0.723277i	$-0.742635\pi$
$241$	−25.8093	−	7.57831i	−1.66253	−	0.488162i	−0.971968	+	0.235115i	$0.924453\pi$
$242$	15.9265	+	4.67645i	1.02380	+	0.300614i
$243$	0.415415	+	0.909632i	0.0266489	+	0.0583529i
$244$	2.34028	−	16.2770i	0.149821	−	1.04203i
$245$	−4.61833	+	5.32983i	−0.295054	+	0.340511i
$246$	−2.36238	+	5.17288i	−0.150620	+	0.329811i
$247$	13.9656	+	8.97518i	0.888613	+	0.571077i
$248$	−0.138868	−	0.965851i	−0.00881815	−	0.0613316i
$249$	−12.9015	+	8.29126i	−0.817597	+	0.525438i
$250$	15.4635	+	17.8459i	0.977999	+	1.12867i
$251$	−5.92489	+	1.73970i	−0.373976	+	0.109809i	−0.463319	−	0.886192i	$-0.653341\pi$
$251$	−5.92489	+	1.73970i	−0.373976	+	0.109809i	0.0893429	+	0.996001i	$0.471523\pi$
$252$	6.28220			0.395741
$253$	−4.24644	+	6.53671i	−0.266971	+	0.410959i
$254$	−36.1777			−2.26999
$255$	−9.12749	+	2.68007i	−0.571585	+	0.167833i
$256$	−11.0402	−	12.7411i	−0.690012	−	0.796316i
$257$	−8.03384	+	5.16304i	−0.501137	+	0.322061i	−0.766671	−	0.642040i	$-0.778088\pi$
$257$	−8.03384	+	5.16304i	−0.501137	+	0.322061i	0.265534	+	0.964102i	$0.414452\pi$
$258$	1.05363	+	7.32815i	0.0655961	+	0.456231i
$259$	21.6691	+	13.9259i	1.34646	+	0.865314i
$260$	−4.29247	+	9.39920i	−0.266208	+	0.582914i
$261$	−5.05844	+	5.83775i	−0.313110	+	0.361348i
$262$	−0.410502	+	2.85510i	−0.0253609	+	0.176389i
$263$	1.19613	+	2.61917i	0.0737568	+	0.161505i	0.942919	−	0.333022i	$-0.108068\pi$
$263$	1.19613	+	2.61917i	0.0737568	+	0.161505i	−0.869162	+	0.494527i	$0.835341\pi$
$264$	0.173610	+	0.0509766i	0.0106850	+	0.00313739i
$265$	2.95421	+	0.867433i	0.181475	+	0.0532860i
$266$	−17.0520	−	37.3387i	−1.04553	−	2.28938i
$267$	0.371749	−	2.58557i	0.0227507	−	0.158234i
$268$	−4.74788	+	5.47935i	−0.290023	+	0.334704i
$269$	3.58458	−	7.84914i	0.218556	−	0.478570i	−0.768317	−	0.640069i	$-0.778906\pi$
$269$	3.58458	−	7.84914i	0.218556	−	0.478570i	0.986873	+	0.161499i	$0.0516329\pi$
$270$	3.42137	+	2.19878i	0.208218	+	0.133813i
$271$	1.06819	+	7.42940i	0.0648877	+	0.451304i	0.996201	+	0.0870845i	$0.0277550\pi$
$271$	1.06819	+	7.42940i	0.0648877	+	0.451304i	−0.931313	+	0.364219i	$0.881336\pi$
$272$	−16.0569	+	10.3191i	−0.973592	+	0.625690i
$273$	5.49301	+	6.33927i	0.332452	+	0.383670i
$274$	8.52776	−	2.50398i	0.515181	−	0.151271i
$275$	−1.31024			−0.0790106
$276$	−5.07879	+	7.81799i	−0.305708	+	0.470588i
$277$	−7.67215			−0.460975			−0.230487	−	0.973075i	$-0.574032\pi$
$277$	−7.67215			−0.460975			−0.230487	+	0.973075i	$0.574032\pi$
$278$	−11.0823	+	3.25405i	−0.664670	+	0.195165i
$279$	5.74006	+	6.62438i	0.343648	+	0.396591i
$280$	−0.619795	+	0.398318i	−0.0370398	+	0.0238041i
$281$	3.28055	+	22.8167i	0.195701	+	1.36113i	0.816584	+	0.577227i	$0.195865\pi$
$281$	3.28055	+	22.8167i	0.195701	+	1.36113i	−0.620882	+	0.783904i	$0.713226\pi$
$282$	−14.5354	−	9.34133i	−0.865570	−	0.556268i
$283$	3.22316	−	7.05774i	0.191597	−	0.419539i	−0.789316	−	0.613988i	$-0.789564\pi$
$283$	3.22316	−	7.05774i	0.191597	−	0.419539i	0.980913	+	0.194449i	$0.0622917\pi$
$284$	1.56996	−	1.81184i	0.0931602	−	0.107513i
$285$	1.86405	−	12.9648i	0.110417	−	0.767966i
$286$	−3.48040	−	7.62101i	−0.205800	−	0.450640i
$287$	8.87914	+	2.60715i	0.524119	+	0.153895i
$288$	7.61598	+	2.23625i	0.448776	+	0.131773i
$289$	1.90161	+	4.16395i	0.111860	+	0.244938i
$290$	−4.47086	+	31.0955i	−0.262538	+	1.82599i
$291$	−0.795566	+	0.918132i	−0.0466369	+	0.0538219i
$292$	9.53784	−	20.8849i	0.558160	−	1.22220i
$293$	8.81117	+	5.66260i	0.514754	+	0.330812i	0.772094	−	0.635509i	$-0.219210\pi$
$293$	8.81117	+	5.66260i	0.514754	+	0.330812i	−0.257340	+	0.966321i	$0.582846\pi$
$294$	−0.973293	−	6.76940i	−0.0567636	−	0.394800i
$295$	8.65810	−	5.56422i	0.504094	−	0.323961i
$296$	0.581062	+	0.670581i	0.0337735	+	0.0389767i
$297$	−1.55951	+	0.457915i	−0.0904922	+	0.0265709i
$298$	−0.0659242			−0.00381888
$299$	−12.3298	+	1.71094i	−0.713051	+	0.0989461i
$300$	−1.56707			−0.0904747
$301$	11.5596	−	3.39419i	0.666282	−	0.195638i
$302$	−19.5887	−	22.6066i	−1.12720	−	1.30086i
$303$	6.40489	−	4.11617i	0.367951	−	0.236468i
$304$	−3.74010	−	26.0130i	−0.214509	−	1.49195i
$305$	−14.5736	−	9.36590i	−0.834483	−	0.536290i
$306$	3.83221	−	8.39137i	0.219073	−	0.479703i
$307$	13.1658	−	15.1941i	0.751409	−	0.867172i	−0.243295	−	0.969952i	$-0.578228\pi$
$307$	13.1658	−	15.1941i	0.751409	−	0.867172i	0.994704	+	0.102780i	$0.0327737\pi$
$308$	−1.45315	+	10.1069i	−0.0828007	+	0.575892i
$309$	4.50444	+	9.86335i	0.256249	+	0.561107i
$310$	34.2044	+	10.0433i	1.94268	+	0.570422i
$311$	16.3900	+	4.81254i	0.929393	+	0.272894i	0.711183	−	0.703007i	$-0.248160\pi$
$311$	16.3900	+	4.81254i	0.929393	+	0.272894i	0.218210	+	0.975902i	$0.429978\pi$
$312$	0.120033	+	0.262837i	0.00679555	+	0.0148802i
$313$	−1.51418	+	10.5314i	−0.0855866	+	0.595268i	0.901220	+	0.433362i	$0.142673\pi$
$313$	−1.51418	+	10.5314i	−0.0855866	+	0.595268i	−0.986806	+	0.161905i	$0.948236\pi$
$314$	20.2966	−	23.4236i	1.14541	−	1.32187i
$315$	2.74927	−	6.02006i	0.154904	−	0.339192i
$316$	14.6985	+	9.44614i	0.826854	+	0.531387i
$317$	−2.24495	−	15.6140i	−0.126089	−	0.876969i	−0.950444	−	0.310896i	$-0.899371\pi$
$317$	−2.24495	−	15.6140i	−0.126089	−	0.876969i	0.824355	−	0.566073i	$-0.191538\pi$
$318$	−2.51179	+	1.61423i	−0.140854	+	0.0905216i
$319$	−8.22175	−	9.48841i	−0.460330	−	0.531249i
$320$	14.8263	−	4.35341i	0.828818	−	0.243363i
$321$	4.59294			0.256353
$322$	27.9345	+	12.9236i	1.55673	+	0.720205i
$323$	−29.7100			−1.65311
$324$	−1.86520	+	0.547672i	−0.103622	+	0.0304262i
$325$	−1.37021	−	1.58131i	−0.0760055	−	0.0877151i
$326$	23.0974	−	14.8438i	1.27925	−	0.822122i
$327$	−0.120157	−	0.835711i	−0.00664470	−	0.0462149i
$328$	0.268173	+	0.172344i	0.0148074	+	0.00951611i
$329$	−11.6800	+	25.5757i	−0.643941	+	1.41003i
$330$	−4.32882	+	4.99573i	−0.238294	+	0.275006i
$331$	1.75458	−	12.2034i	0.0964405	−	0.670759i	−0.883052	−	0.469276i	$-0.844515\pi$
$331$	1.75458	−	12.2034i	0.0964405	−	0.670759i	0.979492	−	0.201483i	$-0.0645760\pi$
$332$	−12.3845	−	27.1182i	−0.679687	−	1.48831i
$333$	−7.64767	−	2.24556i	−0.419090	−	0.123056i
$334$	−4.95979	−	1.45633i	−0.271388	−	0.0796866i
$335$	3.17290	+	6.94769i	0.173354	+	0.379593i
$336$	1.88978	−	13.1437i	0.103096	−	0.717047i
$337$	−19.2495	+	22.2151i	−1.04859	+	1.21013i	−0.0714669	+	0.997443i	$0.522768\pi$
$337$	−19.2495	+	22.2151i	−1.04859	+	1.21013i	−0.977120	+	0.212690i	$0.931777\pi$
$338$	−5.16688	+	11.3139i	−0.281041	+	0.615395i
$339$	9.36405	+	6.01791i	0.508585	+	0.326848i
$340$	−2.63174	−	18.3042i	−0.142726	−	0.992683i
$341$	−11.9851	+	7.70236i	−0.649030	+	0.417106i
$342$	8.31792	+	9.59939i	0.449781	+	0.519075i
$343$	11.0272	−	3.23788i	0.595413	−	0.174829i
$344$	0.415009			0.0223758
$345$	5.26915	+	8.28825i	0.283681	+	0.446225i
$346$	−32.3668			−1.74005
$347$	−28.7698	+	8.44756i	−1.54444	+	0.453489i	−0.939434	−	0.342731i	$-0.888648\pi$
$347$	−28.7698	+	8.44756i	−1.54444	+	0.453489i	−0.605008	+	0.796220i	$0.706830\pi$
$348$	−9.83332	−	11.3483i	−0.527122	−	0.608331i
$349$	7.53619	−	4.84322i	0.403403	−	0.259251i	−0.323170	−	0.946341i	$-0.604748\pi$
$349$	7.53619	−	4.84322i	0.403403	−	0.259251i	0.726573	+	0.687090i	$0.241112\pi$
$350$	0.736287	+	5.12099i	0.0393562	+	0.273728i
$351$	−2.18354	−	1.40328i	−0.116549	−	0.0749013i
$352$	−5.35937	+	11.7354i	−0.285656	+	0.625498i
$353$	6.27244	−	7.23878i	0.333848	−	0.385281i	−0.563861	−	0.825870i	$-0.690685\pi$
$353$	6.27244	−	7.23878i	0.333848	−	0.385281i	0.897709	+	0.440588i	$0.145230\pi$
$354$	−1.42038	+	9.87894i	−0.0754922	+	0.525059i
$355$	−1.04917	−	2.29737i	−0.0556843	−	0.121932i
$356$	4.87220	+	1.43061i	0.258226	+	0.0758221i
$357$	−14.4036	−	4.22928i	−0.762320	−	0.223837i
$358$	−4.73548	−	10.3693i	−0.250278	−	0.548032i
$359$	2.00532	−	13.9473i	0.105837	−	0.736111i	−0.865930	−	0.500166i	$-0.833272\pi$
$359$	2.00532	−	13.9473i	0.105837	−	0.736111i	0.971766	−	0.235945i	$-0.0758185\pi$
$360$	0.149294	−	0.172295i	0.00786849	−	0.00908072i
$361$	9.10060	−	19.9275i	0.478979	−	1.04882i
$362$	19.4487	+	12.4989i	1.02220	+	0.656929i
$363$	1.18950	+	8.27315i	0.0624325	+	0.434228i
$364$	−13.7174	+	8.81565i	−0.718988	+	0.462066i
$365$	−15.8395	−	18.2797i	−0.829075	−	0.956804i
$366$	16.1191	−	4.73299i	0.842558	−	0.247397i
$367$	8.38697			0.437796			0.218898	−	0.975748i	$-0.429754\pi$
$367$	8.38697			0.437796			0.218898	+	0.975748i	$0.429754\pi$
$368$	14.8291	+	12.9777i	0.773022	+	0.676509i
$369$	−2.86353			−0.149069
$370$	−31.1030	+	9.13266i	−1.61697	+	0.474784i
$371$	3.18176	+	3.67195i	0.165189	+	0.190638i
$372$	−14.3343	+	9.21213i	−0.743201	+	0.477626i
$373$	−2.53997	−	17.6659i	−0.131515	−	0.914706i	−0.943581	−	0.331141i	$-0.892566\pi$
$373$	−2.53997	−	17.6659i	−0.131515	−	0.914706i	0.812066	−	0.583565i	$-0.198343\pi$
$374$	12.6137	+	8.10632i	0.652238	+	0.419168i
$375$	−4.93942	+	10.8158i	−0.255071	+	0.558527i
$376$	−0.634263	+	0.731978i	−0.0327096	+	0.0377489i
$377$	2.85333	−	19.8453i	0.146954	−	1.02209i
$378$	2.66609	+	5.83793i	0.137129	+	0.300271i
$379$	21.1535	+	6.21123i	1.08658	+	0.319050i	0.775509	−	0.631336i	$-0.217493\pi$
$379$	21.1535	+	6.21123i	1.08658	+	0.319050i	0.311074	+	0.950386i	$0.399311\pi$
$380$	24.4306	+	7.17346i	1.25326	+	0.367991i
$381$	−7.56760	−	16.5707i	−0.387700	−	0.848945i
$382$	−0.912687	+	6.34788i	−0.0466971	+	0.324786i
$383$	6.06799	−	7.00284i	0.310060	−	0.357828i	−0.579236	−	0.815160i	$-0.696649\pi$
$383$	6.06799	−	7.00284i	0.310060	−	0.357828i	0.889296	+	0.457331i	$0.151195\pi$
$384$	0.369818	−	0.809788i	0.0188722	−	0.0413243i
$385$	9.04919	+	5.81556i	0.461190	+	0.296389i
$386$	−1.23485	−	8.58860i	−0.0628524	−	0.437148i
$387$	−3.13616	+	2.01549i	−0.159420	+	0.102453i
$388$	−1.54654	−	1.78480i	−0.0785135	−	0.0906094i
$389$	−23.3799	+	6.86495i	−1.18541	+	0.348067i	−0.814256	−	0.580506i	$-0.802855\pi$
$389$	−23.3799	+	6.86495i	−1.18541	+	0.348067i	−0.371150	+	0.928573i	$0.621037\pi$
$390$	−10.5562			−0.534533
$391$	16.9077	−	14.5057i	0.855059	−	0.733585i
$392$	−0.383367			−0.0193629
$393$	−1.39361	+	0.409201i	−0.0702983	+	0.0206414i
$394$	27.9296	+	32.2324i	1.40707	+	1.62385i
$395$	15.4845	−	9.95126i	0.779108	−	0.500702i
$396$	−0.449657	−	3.12744i	−0.0225961	−	0.157160i
$397$	23.5996	+	15.1666i	1.18443	+	0.761188i	0.976196	−	0.216891i	$-0.0695916\pi$
$397$	23.5996	+	15.1666i	1.18443	+	0.761188i	0.208235	+	0.978079i	$0.433228\pi$
$398$	5.23417	−	11.4612i	0.262365	−	0.574499i
$399$	13.5356	−	15.6209i	0.677626	−	0.782023i
$400$	−0.471397	+	3.27864i	−0.0235699	+	0.163932i
$401$	5.48424	+	12.0088i	0.273870	+	0.599691i	0.995726	−	0.0923515i	$-0.0294384\pi$
$401$	5.48424	+	12.0088i	0.273870	+	0.599691i	−0.721857	+	0.692042i	$0.756711\pi$
$402$	−7.10680	−	2.08675i	−0.354455	−	0.104077i
$403$	−21.8295	−	6.40971i	−1.08740	−	0.319290i
$404$	6.14824	+	13.4628i	0.305886	+	0.669798i
$405$	−0.291446	+	2.02705i	−0.0144821	+	0.100725i
$406$	−32.4646	+	37.4661i	−1.61119	+	1.85941i
$407$	5.38167	−	11.7842i	0.266760	−	0.584122i
$408$	−0.435025	−	0.279574i	−0.0215370	−	0.0138410i
$409$	−2.81719	−	19.5940i	−0.139301	−	0.968861i	−0.932827	−	0.360324i	$-0.882666\pi$
$409$	−2.81719	−	19.5940i	−0.139301	−	0.968861i	0.793526	−	0.608537i	$-0.208243\pi$
$410$	−9.79718	+	6.29627i	−0.483848	+	0.310950i
$411$	2.93074	+	3.38225i	0.144563	+	0.166834i
$412$	−20.2248	+	5.93854i	−0.996405	+	0.292571i
$413$	16.2411			0.799172
$414$	−9.42050	−	1.40176i	−0.462992	−	0.0688929i
$415$	−31.4065			−1.54168
$416$	−19.7679	+	5.80437i	−0.969199	+	0.284583i
$417$	−3.80864	−	4.39541i	−0.186510	−	0.215244i
$418$	−17.3676	+	11.1615i	−0.849478	+	0.545926i
$419$	−0.651232	−	4.52942i	−0.0318147	−	0.221276i	0.967711	−	0.252061i	$-0.0811084\pi$
$419$	−0.651232	−	4.52942i	−0.0318147	−	0.221276i	−0.999526	+	0.0307848i	$0.990199\pi$
$420$	10.8230	+	6.95549i	0.528106	+	0.339393i
$421$	2.66275	−	5.83061i	0.129774	−	0.284166i	−0.833580	−	0.552399i	$-0.813712\pi$
$421$	2.66275	−	5.83061i	0.129774	−	0.284166i	0.963354	+	0.268233i	$0.0864397\pi$
$422$	19.2032	−	22.1617i	0.934799	−	1.07882i
$423$	1.23818	−	8.61175i	0.0602025	−	0.418717i
$424$	0.0695280	+	0.152245i	0.00337658	+	0.00739367i
$425$	3.59292	+	1.05498i	0.174282	+	0.0511739i
$426$	2.34998	+	0.690016i	0.113857	+	0.0334314i
$427$	−11.3565	−	24.8672i	−0.549578	−	1.20341i
$428$	−1.27065	+	8.83754i	−0.0614190	+	0.427179i
$429$	2.76268	−	3.18830i	0.133383	−	0.153933i
$430$	−6.29835	+	13.7915i	−0.303734	+	0.665084i
$431$	−9.49712	−	6.10343i	−0.457460	−	0.293992i	0.291544	−	0.956558i	$-0.405831\pi$
$431$	−9.49712	−	6.10343i	−0.457460	−	0.293992i	−0.749004	+	0.662566i	$0.769468\pi$
$432$	0.584767	+	4.06715i	0.0281346	+	0.195681i
$433$	−3.84775	+	2.47280i	−0.184911	+	0.118835i	−0.629821	−	0.776740i	$-0.716872\pi$
$433$	−3.84775	+	2.47280i	−0.184911	+	0.118835i	0.444910	+	0.895575i	$0.353236\pi$
$434$	36.8391	+	42.5146i	1.76833	+	2.04077i
$435$	−15.1781	+	4.45669i	−0.727734	+	0.213682i
$436$	1.64128			0.0786031
$437$	8.49696	+	29.4732i	0.406465	+	1.40989i
$438$	23.4557			1.12076
$439$	1.65787	−	0.486795i	0.0791258	−	0.0232334i	−0.241930	−	0.970294i	$-0.577780\pi$
$439$	1.65787	−	0.486795i	0.0791258	−	0.0232334i	0.321056	+	0.947060i	$0.395962\pi$
$440$	0.242656	+	0.280039i	0.0115682	+	0.0133504i
$441$	2.89704	−	1.86182i	0.137954	−	0.0886579i
$442$	3.40762	+	23.7005i	0.162084	+	1.12732i
$443$	9.26899	+	5.95682i	0.440383	+	0.283017i	0.741984	−	0.670417i	$-0.233885\pi$
$443$	9.26899	+	5.95682i	0.440383	+	0.283017i	−0.301601	+	0.953434i	$0.597521\pi$
$444$	6.43655	−	14.0941i	0.305465	−	0.668875i
$445$	3.50313	−	4.04283i	0.166064	−	0.191648i
$446$	5.46768	−	38.0286i	0.258902	−	1.80070i
$447$	−0.0137899	−	0.0301957i	−0.000652240	−	0.00142821i
$448$	23.3967	+	6.86989i	1.10539	+	0.324572i
$449$	−13.0534	−	3.83284i	−0.616030	−	0.180883i	−0.0411937	−	0.999151i	$-0.513116\pi$
$449$	−13.0534	−	3.83284i	−0.616030	−	0.180883i	−0.574836	+	0.818268i	$0.694934\pi$
$450$	−0.665046	−	1.45625i	−0.0313506	−	0.0686482i
$451$	0.662368	−	4.60687i	0.0311897	−	0.216929i
$452$	−14.1700	+	16.3530i	−0.666500	+	0.769182i
$453$	6.25711	−	13.7012i	0.293985	−	0.643737i
$454$	−16.2313	−	10.4312i	−0.761774	−	0.489563i
$455$	2.44467	+	17.0030i	0.114608	+	0.797114i
$456$	0.598981	−	0.384942i	0.0280499	−	0.0180266i
$457$	−16.8885	−	19.4903i	−0.790009	−	0.911719i	0.207780	−	0.978176i	$-0.433376\pi$
$457$	−16.8885	−	19.4903i	−0.790009	−	0.911719i	−0.997789	+	0.0664563i	$0.978831\pi$
$458$	−10.1294	+	2.97427i	−0.473317	+	0.138978i
$459$	4.64517			0.216818
$460$	−17.4056	+	7.84571i	−0.811542	+	0.365808i
$461$	38.6842			1.80170			0.900851	−	0.434129i	$-0.142944\pi$
$461$	38.6842			1.80170			0.900851	+	0.434129i	$0.142944\pi$
$462$	−10.0088	+	2.93885i	−0.465652	+	0.136728i
$463$	−7.06213	−	8.15014i	−0.328205	−	0.378769i	0.567533	−	0.823351i	$-0.307898\pi$
$463$	−7.06213	−	8.15014i	−0.328205	−	0.378769i	−0.895738	+	0.444582i	$0.853352\pi$
$464$	−26.7010	+	17.1597i	−1.23956	+	0.796619i
$465$	2.55461	+	17.7677i	0.118467	+	0.823958i
$466$	−28.1467	−	18.0888i	−1.30387	−	0.837947i
$467$	6.21336	−	13.6054i	0.287520	−	0.629581i	−0.709667	−	0.704538i	$-0.751154\pi$
$467$	6.21336	−	13.6054i	0.287520	−	0.629581i	0.997187	+	0.0749564i	$0.0238818\pi$
$468$	3.30420	−	3.81325i	0.152737	−	0.176268i
$469$	−1.71532	+	11.9303i	−0.0792061	+	0.550890i
$470$	−14.6991	−	32.1864i	−0.678017	−	1.48465i
$471$	14.9745	+	4.39690i	0.689988	+	0.202599i
$472$	0.536804	+	0.157620i	0.0247084	+	0.00725504i
$473$	−2.51711	−	5.51170i	−0.115737	−	0.253428i
$474$	−2.54025	+	17.6679i	−0.116678	+	0.811511i
$475$	−3.37639	+	3.89657i	−0.154920	+	0.178787i
$476$	12.1226	−	26.5448i	0.555638	−	1.21668i
$477$	−1.26479	−	0.812831i	−0.0579107	−	0.0372170i
$478$	−4.02771	−	28.0134i	−0.184223	−	1.28130i
$479$	−35.8617	+	23.0469i	−1.63856	+	1.05304i	−0.696528	+	0.717530i	$0.745273\pi$
$479$	−35.8617	+	23.0469i	−1.63856	+	1.05304i	−0.942036	+	0.335511i	$0.891091\pi$
$480$	10.6449	+	12.2848i	0.485870	+	0.560724i
$481$	19.8501	−	5.82852i	0.905087	−	0.265758i
$482$	53.4196			2.43320
$483$	−0.0761880	+	15.4984i	−0.00346667	+	0.705201i
$484$	−16.2479			−0.738542
$485$	−2.38713	+	0.700926i	−0.108394	+	0.0318274i
$486$	−1.30051	−	1.50087i	−0.0589924	−	0.0680809i
$487$	−27.7611	+	17.8410i	−1.25797	+	0.808451i	−0.988006	−	0.154418i	$-0.950650\pi$
$487$	−27.7611	+	17.8410i	−1.25797	+	0.808451i	−0.269968	+	0.962869i	$0.587013\pi$
$488$	−0.134020	−	0.932129i	−0.00606680	−	0.0421955i
$489$	11.6305	+	7.47446i	0.525949	+	0.338007i
$490$	5.81813	−	12.7399i	0.262836	−	0.575531i
$491$	−19.9564	+	23.0310i	−0.900622	+	1.03937i	0.0983997	+	0.995147i	$0.468628\pi$
$491$	−19.9564	+	23.0310i	−0.900622	+	1.03937i	−0.999022	+	0.0442260i	$0.985918\pi$
$492$	0.792201	−	5.50988i	0.0357152	−	0.248405i
$493$	14.9057	+	32.6389i	0.671318	+	1.46998i
$494$	−31.6331	−	9.28831i	−1.42324	−	0.417901i
$495$	−3.19372	−	0.937761i	−0.143547	−	0.0421492i
$496$	14.9617	+	32.7617i	0.671802	+	1.47104i
$497$	0.567198	−	3.94495i	0.0254423	−	0.176955i
$498$	19.9446	−	23.0173i	0.893741	−	1.03143i
$499$	−11.1079	+	24.3229i	−0.497258	+	1.08884i	0.480092	+	0.877218i	$0.340603\pi$
$499$	−11.1079	+	24.3229i	−0.497258	+	1.08884i	−0.977351	+	0.211626i	$0.932124\pi$
$500$	−19.4449	−	12.4965i	−0.869601	−	0.558858i
$501$	−0.370430	−	2.57640i	−0.0165496	−	0.115105i
$502$	10.3165	−	6.62999i	0.460446	−	0.295911i
$503$	−19.8916	−	22.9561i	−0.886922	−	1.02356i	−0.999552	−	0.0299259i	$-0.990473\pi$
$503$	−19.8916	−	22.9561i	−0.886922	−	1.02356i	0.112630	−	0.993637i	$-0.464073\pi$
$504$	0.345188	−	0.101356i	0.0153759	−	0.00451477i
$505$	15.5917			0.693820
$506$	4.43424	−	14.8315i	0.197126	−	0.659342i
$507$	−6.26298			−0.278149
$508$	33.9783	−	9.97693i	1.50754	−	0.442655i
$509$	−10.9695	−	12.6595i	−0.486215	−	0.561122i	0.458635	−	0.888625i	$-0.348338\pi$
$509$	−10.9695	−	12.6595i	−0.486215	−	0.561122i	−0.944850	+	0.327503i	$0.893793\pi$
$510$	15.8928	−	10.2137i	0.703747	−	0.452271i
$511$	−5.43202	−	37.7806i	−0.240299	−	1.67131i
$512$	26.6678	+	17.1384i	1.17856	+	0.757417i
$513$	−2.65694	+	5.81790i	−0.117307	+	0.256866i
$514$	12.4197	−	14.3331i	0.547809	−	0.632205i
$515$	−3.16021	+	21.9798i	−0.139256	+	0.968545i
$516$	−3.01050	−	6.59207i	−0.132530	−	0.290199i
$517$	13.5683	+	3.98400i	0.596731	+	0.175216i
$518$	−49.0820	−	14.4118i	−2.15654	−	0.633217i
$519$	−6.77044	−	14.8252i	−0.297189	−	0.650754i
$520$	−0.0842127	+	0.585712i	−0.00369297	+	0.0256852i
$521$	7.75531	−	8.95011i	0.339766	−	0.392111i	−0.559993	−	0.828497i	$-0.689196\pi$
$521$	7.75531	−	8.95011i	0.339766	−	0.392111i	0.899760	+	0.436386i	$0.143742\pi$
$522$	6.37258	−	13.9540i	0.278920	−	0.610750i
$523$	7.30361	+	4.69375i	0.319365	+	0.205243i	0.690494	−	0.723338i	$-0.257393\pi$
$523$	7.30361	+	4.69375i	0.319365	+	0.205243i	−0.371130	+	0.928581i	$0.621029\pi$
$524$	−0.401822	−	2.79473i	−0.0175537	−	0.122088i
$525$	−2.19159	+	1.40845i	−0.0956487	+	0.0614697i
$526$	−3.74466	−	4.32156i	−0.163275	−	0.188429i
$527$	39.0671	−	11.4711i	1.70179	−	0.499690i
$528$	−6.67853			−0.290646
$529$	−19.2256	−	12.6244i	−0.835898	−	0.548885i
$530$	−6.11455			−0.265599
$531$	−4.82203	+	1.41588i	−0.209258	+	0.0614437i
$532$	26.3124	+	30.3661i	1.14079	+	1.31654i
$533$	6.25262	−	4.01832i	0.270831	−	0.174053i
$534$	0.738270	+	5.13478i	0.0319481	+	0.222204i
$535$	7.91271	+	5.08519i	0.342096	+	0.219852i
$536$	−0.172479	+	0.377676i	−0.00744994	+	0.0163131i
$537$	3.75894	−	4.33805i	0.162210	−	0.187201i
$538$	−2.43877	+	16.9621i	−0.105143	+	0.731286i
$539$	2.32519	+	5.09145i	0.100153	+	0.219304i
$540$	−3.81973	−	1.12158i	−0.164375	−	0.0482649i
$541$	30.6995	+	9.01419i	1.31988	+	0.387550i	0.864448	−	0.502723i	$-0.167668\pi$
$541$	30.6995	+	9.01419i	1.31988	+	0.387550i	0.455427	+	0.890273i	$0.349486\pi$
$542$	−6.19219	−	13.5590i	−0.265977	−	0.582409i
$543$	−1.65672	+	11.5227i	−0.0710965	+	0.494487i
$544$	24.1454	−	27.8653i	1.03523	−	1.19471i
$545$	0.718272	−	1.57280i	0.0307674	−	0.0673712i
$546$	−14.0137	−	9.00608i	−0.599732	−	0.385425i
$547$	−2.94629	−	20.4919i	−0.125974	−	0.876169i	−0.950584	−	0.310467i	$-0.899514\pi$
$547$	−2.94629	−	20.4919i	−0.125974	−	0.876169i	0.824610	−	0.565702i	$-0.191395\pi$
$548$	−7.31877	+	4.70349i	−0.312643	+	0.200923i
$549$	5.53965	+	6.39309i	0.236426	+	0.272851i
$550$	2.49666	−	0.733085i	0.106458	−	0.0312588i
$551$	−49.4047			−2.10471
$552$	−0.152930	+	0.511516i	−0.00650913	+	0.0217716i
$553$	29.0462			1.23517
$554$	14.6192	−	4.29259i	0.621111	−	0.182375i
$555$	−10.6892	−	12.3360i	−0.453730	−	0.523632i
$556$	9.51113	−	6.11243i	0.403362	−	0.259225i
$557$	3.33433	+	23.1908i	0.141280	+	0.982625i	0.929918	+	0.367767i	$0.119878\pi$
$557$	3.33433	+	23.1908i	0.141280	+	0.982625i	−0.788638	+	0.614858i	$0.789213\pi$
$558$	−14.6440	−	9.41112i	−0.619930	−	0.398405i
$559$	4.01965	−	8.80180i	0.170013	−	0.372277i
$560$	17.8081	−	20.5516i	0.752529	−	0.868464i
$561$	−1.07448	+	7.47320i	−0.0453647	+	0.315519i
$562$	−19.0171	−	41.6416i	−0.802187	−	1.75654i
$563$	18.3162	+	5.37813i	0.771937	+	0.226661i	0.643901	−	0.765109i	$-0.277315\pi$
$563$	18.3162	+	5.37813i	0.771937	+	0.226661i	0.128035	+	0.991770i	$0.459133\pi$
$564$	16.2278	+	4.76492i	0.683314	+	0.200639i
$565$	9.46949	+	20.7353i	0.398384	+	0.872340i
$566$	−2.19288	+	15.2518i	−0.0921737	+	0.641082i
$567$	−2.11630	+	2.44234i	−0.0888761	+	0.102569i
$568$	0.0570329	−	0.124885i	0.00239305	−	0.00524004i
$569$	12.8432	+	8.25385i	0.538417	+	0.346020i	0.781419	−	0.624006i	$-0.214496\pi$
$569$	12.8432	+	8.25385i	0.538417	+	0.346020i	−0.243003	+	0.970026i	$0.578132\pi$
$570$	3.70189	+	25.7472i	0.155055	+	1.07843i
$571$	27.3906	−	17.6029i	1.14626	−	0.736658i	0.177371	−	0.984144i	$-0.443241\pi$
$571$	27.3906	−	17.6029i	1.14626	−	0.736658i	0.968891	+	0.247486i	$0.0796045\pi$
$572$	5.37050	+	6.19788i	0.224552	+	0.259147i
$573$	−3.09848	+	0.909794i	−0.129441	+	0.0380072i
$574$	−18.3778			−0.767076
$575$	0.0190048	−	3.86601i	0.000792554	−	0.161224i
$576$	−7.54545			−0.314394
$577$	−37.1531	+	10.9091i	−1.54670	+	0.454153i	−0.940113	−	0.340863i	$-0.889281\pi$
$577$	−37.1531	+	10.9091i	−1.54670	+	0.454153i	−0.606589	+	0.795015i	$0.707463\pi$
$578$	−5.95325	−	6.87042i	−0.247623	−	0.285772i
$579$	3.67559	−	2.36216i	0.152752	−	0.0981679i
$580$	−4.37632	−	30.4380i	−0.181717	−	1.26387i
$581$	−41.6933	−	26.7947i	−1.72973	−	1.11163i
$582$	1.00225	−	2.19462i	0.0415445	−	0.0909697i
$583$	1.60025	−	1.84679i	0.0662756	−	0.0764862i
$584$	0.187120	−	1.30145i	0.00774308	−	0.0538543i
$585$	−2.20813	−	4.83512i	−0.0912947	−	0.199908i
$586$	−19.9579	−	5.86016i	−0.824452	−	0.242081i
$587$	4.61318	+	1.35455i	0.190406	+	0.0559083i	0.375545	−	0.926804i	$-0.377455\pi$
$587$	4.61318	+	1.35455i	0.190406	+	0.0559083i	−0.185139	+	0.982712i	$0.559274\pi$
$588$	2.78096	+	6.08944i	0.114685	+	0.251124i
$589$	−7.97843	+	55.4912i	−0.328746	+	2.28648i
$590$	−13.3847	+	15.4468i	−0.551041	+	0.635935i
$591$	−8.92138	+	19.5351i	−0.366976	+	0.803566i
$592$	−27.5516	−	17.7063i	−1.13236	−	0.727726i
$593$	4.47077	+	31.0949i	0.183593	+	1.27691i	0.848182	+	0.529706i	$0.177698\pi$
$593$	4.47077	+	31.0949i	0.183593	+	1.27691i	−0.664589	+	0.747209i	$0.731393\pi$
$594$	2.71544	−	1.74511i	0.111416	−	0.0716026i
$595$	−20.1320	−	23.2335i	−0.825330	−	0.952481i
$596$	0.0619163	−	0.0181803i	0.00253619	−	0.000744692i
$597$	6.34454			0.259665
$598$	22.5371	−	10.1587i	0.921610	−	0.415422i
$599$	38.0521			1.55477			0.777384	−	0.629026i	$-0.216546\pi$
$599$	38.0521			1.55477			0.777384	+	0.629026i	$0.216546\pi$
$600$	−0.0861057	+	0.0252829i	−0.00351525	+	0.00103217i
$601$	4.36534	+	5.03788i	0.178066	+	0.205499i	0.837765	−	0.546031i	$-0.183862\pi$
$601$	4.36534	+	5.03788i	0.178066	+	0.205499i	−0.659699	+	0.751530i	$0.729316\pi$
$602$	−20.1276	+	12.9352i	−0.820340	+	0.527200i
$603$	−0.530783	−	3.69168i	−0.0216152	−	0.150337i
$604$	24.6322	+	15.8301i	1.00227	+	0.644119i
$605$	−7.11056	+	15.5700i	−0.289085	+	0.633009i
$606$	−9.90146	+	11.4269i	−0.402219	+	0.464186i
$607$	−0.942420	+	6.55468i	−0.0382517	+	0.266046i	−0.999968	−	0.00800074i	$-0.997453\pi$
$607$	−0.942420	+	6.55468i	−0.0382517	+	0.266046i	0.961716	+	0.274047i	$0.0883623\pi$
$608$	21.0895	+	46.1796i	0.855292	+	1.87283i
$609$	−23.9517	−	7.03287i	−0.970574	−	0.284986i
$610$	33.0102	+	9.69266i	1.33654	+	0.392444i
$611$	9.38103	+	20.5416i	0.379516	+	0.831024i
$612$	−1.28510	+	8.93804i	−0.0519469	+	0.361299i
$613$	−19.4706	+	22.4703i	−0.786410	+	0.907565i	−0.997555	−	0.0698897i	$-0.977735\pi$
$613$	−19.4706	+	22.4703i	−0.786410	+	0.907565i	0.211145	+	0.977455i	$0.432281\pi$
$614$	−16.5861	+	36.3185i	−0.669361	+	1.46570i
$615$	−4.93328	−	3.17043i	−0.198929	−	0.127844i
$616$	0.0832169	+	0.578786i	0.00335291	+	0.0233200i
$617$	40.9365	−	26.3083i	1.64804	−	1.05913i	0.715156	−	0.698965i	$-0.246356\pi$
$617$	40.9365	−	26.3083i	1.64804	−	1.05913i	0.932888	−	0.360168i	$-0.117281\pi$
$618$	−14.1018	−	16.2743i	−0.567256	−	0.654648i
$619$	−25.4383	+	7.46935i	−1.02245	+	0.300219i	−0.749638	−	0.661849i	$-0.769772\pi$
$619$	−25.4383	+	7.46935i	−1.02245	+	0.300219i	−0.272813	+	0.962067i	$0.587954\pi$
$620$	−34.8946			−1.40140
$621$	−1.32851	−	4.60815i	−0.0533111	−	0.184919i
$622$	−33.9237			−1.36022
$623$	8.09971	−	2.37829i	0.324508	−	0.0952841i
$624$	−6.98419	−	8.06018i	−0.279591	−	0.322665i
$625$	−17.0939	+	10.9856i	−0.683755	+	0.439422i
$626$	−3.00707	−	20.9146i	−0.120187	−	0.835916i
$627$	−8.74530	−	5.62026i	−0.349254	−	0.224452i
$628$	−12.6031	+	27.5969i	−0.502917	+	1.10123i
$629$	−24.2459	+	27.9812i	−0.966746	+	1.11568i
$630$	−1.87047	+	13.0094i	−0.0745213	+	0.518307i
$631$	12.5343	+	27.4463i	0.498982	+	1.09262i	0.976799	+	0.214159i	$0.0687012\pi$
$631$	12.5343	+	27.4463i	0.498982	+	1.09262i	−0.477816	+	0.878460i	$0.658572\pi$
$632$	0.960040	+	0.281893i	0.0381883	+	0.0112131i
$633$	14.1678	+	4.16003i	0.563119	+	0.165347i
$634$	13.0138	+	28.4963i	0.516844	+	1.13173i
$635$	5.30926	−	36.9267i	0.210692	−	1.46539i
$636$	1.91392	−	2.20878i	0.0758919	−	0.0875840i
$637$	−3.71317	+	8.13070i	−0.147121	+	0.322150i
$638$	20.9753	+	13.4800i	0.830419	+	0.533678i
$639$	0.175512	+	1.22071i	0.00694315	+	0.0482907i
$640$	1.53370	−	0.985648i	0.0606247	−	0.0389612i
$641$	28.2677	+	32.6226i	1.11651	+	1.28852i	0.953334	+	0.301918i	$0.0976269\pi$
$641$	28.2677	+	32.6226i	1.11651	+	1.28852i	0.163171	+	0.986598i	$0.447828\pi$
$642$	−8.75182	+	2.56976i	−0.345407	+	0.101421i
$643$	−7.57458			−0.298712			−0.149356	−	0.988783i	$-0.547720\pi$
$643$	−7.57458			−0.298712			−0.149356	+	0.988783i	$0.547720\pi$
$644$	−29.8003	−	4.43426i	−1.17429	−	0.174734i
$645$	−7.63448			−0.300607
$646$	56.6121	−	16.6228i	2.22737	−	0.654016i
$647$	−16.9543	−	19.5663i	−0.666541	−	0.769230i	0.317290	−	0.948329i	$-0.397227\pi$
$647$	−16.9543	−	19.5663i	−0.666541	−	0.769230i	−0.983831	+	0.179099i	$0.942682\pi$
$648$	−0.0936511	+	0.0601859i	−0.00367896	+	0.00236433i
$649$	−1.16248	−	8.08523i	−0.0456314	−	0.317373i
$650$	3.49567	+	2.24653i	0.137111	+	0.0881162i
$651$	−11.7673	+	25.7668i	−0.461197	+	1.00988i
$652$	−17.5996	+	20.3111i	−0.689255	+	0.795442i
$653$	6.40456	−	44.5447i	0.250630	−	1.74317i	−0.343819	−	0.939036i	$-0.611721\pi$
$653$	6.40456	−	44.5447i	0.250630	−	1.74317i	0.594449	−	0.804134i	$-0.297370\pi$
$654$	0.696541	+	1.52521i	0.0272369	+	0.0596405i
$655$	−2.85397	−	0.838000i	−0.111514	−	0.0327434i
$656$	−11.2895	−	3.31491i	−0.440782	−	0.129425i
$657$	4.90644	+	10.7436i	0.191418	+	0.419148i
$658$	7.94653	−	55.2693i	0.309788	−	2.15462i
$659$	20.2462	−	23.3653i	0.788679	−	0.910184i	−0.209025	−	0.977910i	$-0.567029\pi$
$659$	20.2462	−	23.3653i	0.788679	−	0.910184i	0.997704	+	0.0677265i	$0.0215745\pi$
$660$	2.68795	−	5.88579i	0.104628	−	0.229104i
$661$	−9.43193	−	6.06153i	−0.366860	−	0.235766i	0.344203	−	0.938895i	$-0.388149\pi$
$661$	−9.43193	−	6.06153i	−0.366860	−	0.235766i	−0.711062	+	0.703129i	$0.751786\pi$
$662$	3.48449	+	24.2351i	0.135428	+	0.941926i
$663$	−10.1429	+	6.51845i	−0.393918	+	0.253156i
$664$	−1.11801	−	1.29026i	−0.0433873	−	0.0500716i
$665$	40.6141	−	11.9254i	1.57495	−	0.462447i
$666$	15.8290			0.613360
$667$	28.1158	−	24.1215i	1.08865	−	0.933988i
$668$	5.05988			0.195773
$669$	18.5622	−	5.45035i	0.717656	−	0.210723i
$670$	−9.93320	−	11.4635i	−0.383753	−	0.442874i
$671$	−11.5667	+	7.43344i	−0.446526	+	0.286965i
$672$	3.65058	+	25.3903i	0.140824	+	0.979454i
$673$	5.55352	+	3.56903i	0.214073	+	0.137576i	0.643283	−	0.765628i	$-0.277572\pi$
$673$	5.55352	+	3.56903i	0.214073	+	0.137576i	−0.429211	+	0.903204i	$0.641208\pi$
$674$	24.2503	−	53.1008i	0.934088	−	2.04537i
$675$	0.527902	−	0.609231i	0.0203189	−	0.0234493i
$676$	1.73267	−	12.0510i	0.0666410	−	0.463498i
$677$	−12.0749	−	26.4404i	−0.464076	−	1.01619i	−0.986539	−	0.163524i	$-0.947714\pi$
$677$	−12.0749	−	26.4404i	−0.464076	−	1.01619i	0.522463	−	0.852662i	$-0.325013\pi$
$678$	−21.2102	−	6.22787i	−0.814571	−	0.239180i
$679$	−3.76701	−	1.10609i	−0.144565	−	0.0424480i
$680$	−0.439924	−	0.963299i	−0.0168703	−	0.0369408i
$681$	1.38265	−	9.61654i	0.0529832	−	0.368507i
$682$	18.5280	−	21.3825i	0.709475	−	0.818778i
$683$	−5.13709	+	11.2487i	−0.196565	+	0.430418i	−0.982090	−	0.188412i	$-0.939666\pi$
$683$	−5.13709	+	11.2487i	−0.196565	+	0.430418i	0.785525	+	0.618830i	$0.212393\pi$
$684$	−10.4595	−	6.72191i	−0.399929	−	0.257019i
$685$	1.30432	+	9.07177i	0.0498357	+	0.346615i
$686$	−19.2006	+	12.3395i	−0.733084	+	0.471124i
$687$	−3.48118	−	4.01749i	−0.132815	−	0.153277i
$688$	−14.6976	+	4.31561i	−0.560341	+	0.164531i
$689$	3.90234			0.148667
$690$	−14.6776	−	12.8451i	−0.558767	−	0.489005i
$691$	28.7504			1.09372			0.546858	−	0.837225i	$-0.315824\pi$
$691$	28.7504			1.09372			0.546858	+	0.837225i	$0.315824\pi$
$692$	30.3991	−	8.92597i	1.15560	−	0.339314i
$693$	−3.43973	−	3.96966i	−0.130665	−	0.150795i
$694$	50.0941	−	32.1935i	1.90155	−	1.22205i
$695$	−1.69504	−	11.7892i	−0.0642964	−	0.447191i
$696$	−0.723403	−	0.464903i	−0.0274205	−	0.0176221i
$697$	−5.52567	+	12.0995i	−0.209300	+	0.458303i
$698$	−11.6504	+	13.4452i	−0.440973	+	0.508910i
$699$	2.39765	−	16.6760i	0.0906874	−	0.630745i
$700$	−2.10377	−	4.60661i	−0.0795149	−	0.174113i
$701$	−27.4145	−	8.04963i	−1.03543	−	0.304030i	−0.280515	−	0.959850i	$-0.590505\pi$
$701$	−27.4145	−	8.04963i	−1.03543	−	0.304030i	−0.754918	+	0.655819i	$0.772323\pi$
$702$	4.94585	+	1.45223i	0.186669	+	0.0548110i
$703$	−21.1772	−	46.3717i	−0.798715	−	1.74894i
$704$	1.74535	−	12.1392i	0.0657804	−	0.457513i
$705$	11.6679	−	13.4654i	0.439437	−	0.507137i
$706$	−7.90196	+	17.3029i	−0.297394	+	0.651202i
$707$	20.6985	+	13.3021i	0.778448	+	0.500278i
$708$	−1.39034	−	9.67005i	−0.0522523	−	0.363423i
$709$	23.0015	−	14.7822i	0.863840	−	0.555156i	−0.0320229	−	0.999487i	$-0.510195\pi$
$709$	23.0015	−	14.7822i	0.863840	−	0.555156i	0.895863	+	0.444331i	$0.146559\pi$
$710$	3.28457	+	3.79060i	0.123268	+	0.142259i
$711$	−8.62389	+	2.53220i	−0.323421	+	0.0949651i
$712$	0.290794			0.0108980
$713$	−22.5528	−	35.4750i	−0.844608	−	1.32855i
$714$	29.8123			1.11570
$715$	8.28955	−	2.43403i	0.310012	−	0.0910276i
$716$	7.30717	+	8.43292i	0.273082	+	0.315153i
$717$	11.9886	−	7.70463i	0.447724	−	0.287735i
$718$	3.98244	+	27.6985i	0.148623	+	1.03370i
$719$	−28.0260	−	18.0112i	−1.04519	−	0.671704i	−0.0989264	−	0.995095i	$-0.531541\pi$
$719$	−28.0260	−	18.0112i	−1.04519	−	0.671704i	−0.946266	+	0.323391i	$0.895177\pi$
$720$	−3.49561	+	7.65431i	−0.130274	+	0.285259i
$721$	−22.9475	+	26.4828i	−0.854610	+	0.986272i
$722$	−6.19161	+	43.0636i	−0.230428	+	1.60266i
$723$	11.1742	+	24.4681i	0.415574	+	0.909980i
$724$	−21.7132	−	6.37557i	−0.806965	−	0.236946i
$725$	5.97466	+	1.75432i	0.221893	+	0.0651538i
$726$	−6.89544	−	15.0989i	−0.255914	−	0.560373i
$727$	3.27954	−	22.8097i	0.121632	−	0.845966i	−0.834076	−	0.551649i	$-0.813999\pi$
$727$	3.27954	−	22.8097i	0.121632	−	0.845966i	0.955708	−	0.294317i	$-0.0950921\pi$
$728$	−0.611500	+	0.705709i	−0.0226637	+	0.0261553i
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$	40.4095	+	25.9696i	1.49562	+	0.961179i
$731$	2.46447	+	17.1408i	0.0911518	+	0.633975i
$732$	−13.8339	+	8.89049i	−0.511315	+	0.328602i
$733$	6.62114	+	7.64120i	0.244557	+	0.282234i	0.864736	−	0.502226i	$-0.167485\pi$
$733$	6.62114	+	7.64120i	0.244557	+	0.282234i	−0.620179	+	0.784460i	$0.712940\pi$
$734$	−15.9813	+	4.69254i	−0.589881	+	0.173205i
$735$	7.05238			0.260131
$736$	−34.5488	−	15.9836i	−1.27348	−	0.589164i
$737$	6.06199			0.223296
$738$	5.45643	−	1.60215i	0.200854	−	0.0589760i
$739$	−3.15006	−	3.63536i	−0.115877	−	0.133729i	0.694847	−	0.719157i	$-0.255472\pi$
$739$	−3.15006	−	3.63536i	−0.115877	−	0.133729i	−0.810724	+	0.585428i	$0.800926\pi$
$740$	26.6935	−	17.1549i	0.981272	−	0.630626i
$741$	−2.36257	−	16.4320i	−0.0867911	−	0.603645i
$742$	−8.11730	−	5.21667i	−0.297995	−	0.191510i
$743$	−11.0854	+	24.2735i	−0.406682	+	0.890510i	0.589867	+	0.807501i	$0.299180\pi$
$743$	−11.0854	+	24.2735i	−0.406682	+	0.890510i	−0.996549	+	0.0830089i	$0.973547\pi$
$744$	−0.639002	+	0.737448i	−0.0234269	+	0.0270361i
$745$	0.00967469	−	0.0672889i	0.000354453	−	0.00246528i
$746$	14.7240	+	32.2411i	0.539085	+	1.18043i
$747$	14.7148	+	4.32065i	0.538386	+	0.158084i
$748$	−14.0823	−	4.13495i	−0.514902	−	0.151189i
$749$	6.16596	+	13.5016i	0.225299	+	0.493337i
$750$	3.36055	−	23.3731i	0.122710	−	0.853465i
$751$	−13.6470	+	15.7495i	−0.497987	+	0.574707i	−0.947982	−	0.318323i	$-0.896880\pi$
$751$	−13.6470	+	15.7495i	−0.497987	+	0.574707i	0.449995	+	0.893031i	$0.351426\pi$
$752$	14.8508	−	32.5187i	0.541552	−	1.18583i
$753$	5.19476	+	3.33847i	0.189308	+	0.121661i
$754$	5.66653	+	39.4116i	0.206363	+	1.43529i
$755$	25.9493	−	16.6766i	0.944393	−	0.606925i
$756$	−4.11396	−	4.74777i	−0.149623	−	0.172675i
$757$	−14.0513	+	4.12582i	−0.510701	+	0.149955i	−0.526923	−	0.849913i	$-0.676654\pi$
$757$	−14.0513	+	4.12582i	−0.510701	+	0.149955i	0.0162217	+	0.999868i	$0.494836\pi$
$758$	−43.7831			−1.59027
$759$	7.72094	−	1.07139i	0.280252	−	0.0388890i
$760$	1.45812			0.0528916
$761$	−23.8070	+	6.99036i	−0.863003	+	0.253400i	−0.683137	−	0.730291i	$-0.739385\pi$
$761$	−23.8070	+	6.99036i	−0.863003	+	0.253400i	−0.179866	+	0.983691i	$0.557566\pi$
$762$	23.6914	+	27.3413i	0.858248	+	0.990471i
$763$	2.29537	−	1.47515i	0.0830982	−	0.0534039i
$764$	−0.893388	−	6.21365i	−0.0323217	−	0.224802i
$765$	8.00269	+	5.14302i	0.289338	+	0.185946i
$766$	−7.64440	+	16.7389i	−0.276204	+	0.604801i
$767$	8.54222	−	9.85825i	0.308442	−	0.355961i
$768$	−2.39926	+	16.6872i	−0.0865760	+	0.602149i
$769$	−11.3732	−	24.9037i	−0.410126	−	0.898052i	−0.996142	−	0.0877520i	$-0.972032\pi$
$769$	−11.3732	−	24.9037i	−0.410126	−	0.898052i	0.586016	−	0.810300i	$-0.300696\pi$
$770$	−20.4970	−	6.01846i	−0.738660	−	0.216890i
$771$	9.16301	+	2.69050i	0.329998	+	0.0968961i
$772$	3.52830	+	7.72591i	0.126986	+	0.278062i
$773$	1.28113	−	8.91045i	0.0460790	−	0.320487i	−0.953725	−	0.300681i	$-0.902786\pi$
$773$	1.28113	−	8.91045i	0.0460790	−	0.320487i	0.999804	−	0.0198058i	$-0.00630479\pi$
$774$	4.84826	−	5.59520i	0.174267	−	0.201115i
$775$	2.93531	−	6.42742i	0.105439	−	0.230880i
$776$	−0.113773	−	0.0731176i	−0.00408422	−	0.00262477i
$777$	−3.66577	−	25.4960i	−0.131509	−	0.914663i
$778$	40.7092	−	26.1622i	1.45950	−	0.937960i
$779$	−11.9936	−	13.8414i	−0.429716	−	0.495919i
$780$	9.91442	−	2.91114i	0.354993	−	0.104235i
$781$	−2.00449			−0.0717264
$782$	−24.1015	+	37.1004i	−0.861868	+	1.32671i
$783$	7.72445			0.276049
$784$	13.5770	−	3.98656i	0.484892	−	0.142377i
$785$	20.9299	+	24.1544i	0.747019	+	0.862106i
$786$	2.42656	−	1.55946i	0.0865526	−	0.0556240i
$787$	3.09178	+	21.5038i	0.110210	+	0.766528i	0.967714	+	0.252050i	$0.0811049\pi$
$787$	3.09178	+	21.5038i	0.110210	+	0.766528i	−0.857504	+	0.514477i	$0.827986\pi$
$788$	−35.1205	−	22.5706i	−1.25111	−	0.804043i
$789$	1.19613	−	2.61917i	0.0425835	−	0.0932448i
$790$	−23.9378	+	27.6256i	−0.851667	+	0.982876i
$791$	−5.11935	+	35.6058i	−0.182023	+	1.26600i
$792$	−0.0751651	−	0.164589i	−0.00267087	−	0.00584840i
$793$	−21.0673	−	6.18592i	−0.748122	−	0.219668i
$794$	−53.4546	−	15.6957i	−1.89703	−	0.557020i
$795$	−1.27903	−	2.80069i	−0.0453626	−	0.0993302i
$796$	−1.75523	+	12.2079i	−0.0622125	+	0.432697i
$797$	−18.8971	+	21.8084i	−0.669369	+	0.772493i	−0.984277	−	0.176629i	$-0.943481\pi$
$797$	−18.8971	+	21.8084i	−0.669369	+	0.772493i	0.314909	+	0.949122i	$0.398026\pi$
$798$	−17.0520	+	37.3387i	−0.603634	+	1.32177i
$799$	−33.9988	−	21.8497i	−1.20279	−	0.772986i
$800$	−0.910622	−	6.33352i	−0.0321954	−	0.223924i
$801$	−2.19749	+	1.41224i	−0.0776444	+	0.0498991i
$802$	−17.1691	−	19.8142i	−0.606263	−	0.699665i
$803$	−18.4193	+	5.40840i	−0.650003	+	0.190858i
$804$	7.25022			0.255695
$805$	−17.2907	+	26.6162i	−0.609416	+	0.938099i
$806$	45.1821			1.59147
$807$	−8.27938	+	2.43105i	−0.291448	+	0.0855769i
$808$	0.555034	+	0.640544i	0.0195260	+	0.0225342i
$809$	29.2641	−	18.8069i	1.02887	−	0.661215i	0.0866604	−	0.996238i	$-0.472380\pi$
$809$	29.2641	−	18.8069i	1.02887	−	0.661215i	0.942210	+	0.335023i	$0.108744\pi$
$810$	−0.578793	−	4.02559i	−0.0203367	−	0.141445i
$811$	9.27718	+	5.96208i	0.325766	+	0.209357i	0.693293	−	0.720656i	$-0.256159\pi$
$811$	9.27718	+	5.96208i	0.325766	+	0.209357i	−0.367527	+	0.930013i	$0.619796\pi$
$812$	20.1586	−	44.1413i	0.707430	−	1.54905i
$813$	4.91525	−	5.67250i	0.172385	−	0.198943i
$814$	−3.66143	+	25.4658i	−0.128333	+	0.892576i
$815$	11.7614	+	25.7540i	0.411985	+	0.902122i
$816$	18.3137	+	5.37739i	0.641108	+	0.188246i
$817$	−22.8778	−	6.71752i	−0.800392	−	0.235016i
$818$	16.3310	+	35.7600i	0.571001	+	1.25032i
$819$	1.19375	−	8.30268i	0.0417128	−	0.290119i
$820$	7.46520	−	8.61530i	0.260696	−	0.300860i
$821$	5.73009	−	12.5471i	0.199981	−	0.437898i	−0.782898	−	0.622151i	$-0.786259\pi$
$821$	5.73009	−	12.5471i	0.199981	−	0.437898i	0.982879	+	0.184252i	$0.0589864\pi$
$822$	−7.47687	−	4.80509i	−0.260786	−	0.167597i
$823$	3.55362	+	24.7160i	0.123871	+	0.861545i	0.953104	+	0.302642i	$0.0978686\pi$
$823$	3.55362	+	24.7160i	0.123871	+	0.861545i	−0.829233	+	0.558903i	$0.811222\pi$
$824$	−1.01548	+	0.652610i	−0.0353760	+	0.0227347i
$825$	0.858027	+	0.990215i	0.0298727	+	0.0344749i
$826$	−30.9473	+	9.08695i	−1.07679	+	0.316175i
$827$	−29.2203			−1.01609			−0.508045	−	0.861331i	$-0.669631\pi$
$827$	−29.2203			−1.01609			−0.508045	+	0.861331i	$0.669631\pi$
$828$	9.23435	−	1.28140i	0.320916	−	0.0445317i
$829$	16.9029			0.587063			0.293531	−	0.955949i	$-0.405169\pi$
$829$	16.9029			0.587063			0.293531	+	0.955949i	$0.405169\pi$
$830$	59.8448	−	17.5720i	2.07724	−	0.609934i
$831$	5.02419	+	5.79823i	0.174287	+	0.201138i
$832$	16.4758	−	10.5883i	0.571195	−	0.367084i
$833$	−2.27657	−	15.8339i	−0.0788783	−	0.548611i
$834$	9.71659	+	6.24447i	0.336458	+	0.216228i
$835$	2.21435	−	4.84875i	0.0766307	−	0.167798i
$836$	13.2337	−	15.2725i	0.457696	−	0.528210i
$837$	1.24743	−	8.67609i	0.0431176	−	0.299890i
$838$	3.77514	+	8.26640i	0.130410	+	0.285558i
$839$	1.52515	+	0.447825i	0.0526540	+	0.0154606i	0.307953	−	0.951401i	$-0.400356\pi$
$839$	1.52515	+	0.447825i	0.0526540	+	0.0154606i	−0.255299	+	0.966862i	$0.582174\pi$
$840$	0.706908	+	0.207567i	0.0243907	+	0.00716174i
$841$	12.7396	+	27.8958i	0.439296	+	0.961925i
$842$	−1.81161	+	12.6000i	−0.0624320	+	0.434224i
$843$	15.0954	−	17.4210i	0.519914	−	0.600013i
$844$	−11.9241	+	26.1102i	−0.410445	+	0.898749i
$845$	−10.7899	−	6.93422i	−0.371182	−	0.238544i
$846$	2.45895	+	17.1024i	0.0845405	+	0.587992i
$847$	−22.7232	+	14.6033i	−0.780777	+	0.501775i
$848$	−4.04551	−	4.66877i	−0.138923	−	0.160326i
$849$	−7.44460	+	2.18593i	−0.255498	+	0.0750210i
$850$	−7.43654			−0.255071
$851$	34.6925	+	16.0501i	1.18924	+	0.550191i
$852$	−2.39740			−0.0821336
$853$	−17.4876	+	5.13482i	−0.598764	+	0.175813i	−0.567049	−	0.823684i	$-0.691915\pi$
$853$	−17.4876	+	5.13482i	−0.598764	+	0.175813i	−0.0317146	+	0.999497i	$0.510097\pi$
$854$	35.5529	+	41.0302i	1.21660	+	1.40403i
$855$	−11.0188	+	7.08136i	−0.376835	+	0.242177i
$856$	0.0727658	+	0.506097i	0.00248708	+	0.0172980i
$857$	−25.8396	−	16.6061i	−0.882665	−	0.567254i	0.0189372	−	0.999821i	$-0.493972\pi$
$857$	−25.8396	−	16.6061i	−0.882665	−	0.567254i	−0.901602	+	0.432566i	$0.857608\pi$
$858$	−3.48040	+	7.62101i	−0.118819	+	0.260177i
$859$	−7.22996	+	8.34382i	−0.246683	+	0.284687i	−0.865565	−	0.500797i	$-0.833040\pi$
$859$	−7.22996	+	8.34382i	−0.246683	+	0.284687i	0.618882	+	0.785484i	$0.287586\pi$
$860$	2.11210	−	14.6899i	0.0720219	−	0.500923i
$861$	−3.84425	−	8.41773i	−0.131012	−	0.286875i
$862$	21.5116	+	6.31637i	0.732687	+	0.215136i
$863$	−15.3401	−	4.50427i	−0.522184	−	0.153327i	0.0100093	−	0.999950i	$-0.496814\pi$
$863$	−15.3401	−	4.50427i	−0.522184	−	0.153327i	−0.532193	+	0.846623i	$0.678632\pi$
$864$	−3.29736	−	7.22021i	−0.112178	−	0.245637i
$865$	4.74999	−	33.0369i	0.161504	−	1.12329i
$866$	5.94832	−	6.86473i	0.202132	−	0.233273i
$867$	1.90161	−	4.16395i	0.0645821	−	0.141415i
$868$	−46.3239	−	29.7706i	−1.57234	−	1.01048i
$869$	−2.07902	−	14.4599i	−0.0705261	−	0.490520i
$870$	26.4282	−	16.9844i	0.896000	−	0.575824i
$871$	6.33943	+	7.31609i	0.214803	+	0.247896i
$872$	0.0901835	−	0.0264803i	0.00305400	−	0.000896735i
$873$	1.21486			0.0411169
$874$	−32.6812	−	51.4069i	−1.10546	−	1.73886i
$875$	−38.4257			−1.29903
$876$	−22.0297	+	6.46852i	−0.744316	+	0.218551i
$877$	21.6818	+	25.0221i	0.732143	+	0.844938i	0.992711	−	0.120518i	$-0.0384554\pi$
$877$	21.6818	+	25.0221i	0.732143	+	0.844938i	−0.260569	+	0.965455i	$0.583910\pi$
$878$	−2.88670	+	1.85517i	−0.0974213	+	0.0626088i
$879$	−1.49059	−	10.3673i	−0.0502762	−	0.349679i
$880$	−11.5058	−	7.39430i	−0.387859	−	0.249262i
$881$	−13.8057	+	30.2303i	−0.465126	+	1.01848i	0.521163	+	0.853457i	$0.325498\pi$
$881$	−13.8057	+	30.2303i	−0.465126	+	1.01848i	−0.986289	+	0.165027i	$0.947229\pi$
$882$	−4.47860	+	5.16858i	−0.150802	+	0.174035i
$883$	4.21852	−	29.3404i	0.141964	−	0.987384i	−0.786931	−	0.617041i	$-0.788331\pi$
$883$	4.21852	−	29.3404i	0.141964	−	0.987384i	0.928895	−	0.370343i	$-0.120760\pi$
$884$	−9.73647	−	21.3199i	−0.327473	−	0.717066i
$885$	−9.87500	−	2.89956i	−0.331945	−	0.0974677i
$886$	−20.9948	−	6.16464i	−0.705336	−	0.207105i
$887$	4.09687	+	8.97089i	0.137559	+	0.301213i	0.965857	−	0.259075i	$-0.0834177\pi$
$887$	4.09687	+	8.97089i	0.137559	+	0.301213i	−0.828298	+	0.560288i	$0.810690\pi$
$888$	0.126277	−	0.878274i	0.00423757	−	0.0294729i
$889$	38.5525	−	44.4920i	1.29301	−	1.49221i
$890$	−4.41321	+	9.66359i	−0.147931	+	0.323924i
$891$	1.36733	+	0.878732i	0.0458074	+	0.0294386i
$892$	5.35207	+	37.2244i	0.179200	+	1.24637i
$893$	46.8125	−	30.0845i	1.56652	−	1.00674i
$894$	0.0431711	+	0.0498222i	0.00144386	+	0.00166630i
$895$	11.2789	−	3.31178i	0.377011	−	0.110700i
$896$	2.87695			0.0961123
$897$	9.36735	+	8.19782i	0.312767	+	0.273717i
$898$	27.0177			0.901593
$899$	64.9646	−	19.0753i	2.16669	−	0.636198i
$900$	1.02621	+	1.18431i	0.0342070	+	0.0394770i
$901$	−5.87517	+	3.77574i	−0.195730	+	0.125788i
$902$	1.31542	+	9.14895i	0.0437987	+	0.304627i
$903$	−10.1351	−	6.51341i	−0.337274	−	0.216753i
$904$	−0.514760	+	1.12717i	−0.0171207	+	0.0374890i
$905$	−15.6119	+	18.0171i	−0.518956	+	0.598907i
$906$	−4.25704	+	29.6083i	−0.141431	+	0.983671i
$907$	16.2239	+	35.5254i	0.538705	+	1.17960i	0.961860	+	0.273543i	$0.0881955\pi$
$907$	16.2239	+	35.5254i	0.538705	+	1.17960i	−0.423154	+	0.906058i	$0.639077\pi$
$908$	18.1212	+	5.32087i	0.601374	+	0.176579i
$909$	−7.30511	−	2.14497i	−0.242295	−	0.0711443i
$910$	−14.1715	−	31.0313i	−0.469782	−	1.02868i
$911$	−1.22251	+	8.50273i	−0.0405035	+	0.281708i	−1.00000		1.24817e-5i	$-0.999996\pi$
$911$	−1.22251	+	8.50273i	−0.0405035	+	0.281708i	0.959496	+	0.281721i	$0.0909051\pi$
$912$	−17.2100	+	19.8615i	−0.569882	+	0.657678i
$913$	−10.3548	+	22.6739i	−0.342694	+	0.750395i
$914$	43.0857	+	27.6895i	1.42515	+	0.915888i
$915$	2.46542	+	17.1474i	0.0815043	+	0.566875i
$916$	8.69337	−	5.58689i	0.287237	−	0.184596i
$917$	−3.07380	−	3.54736i	−0.101506	−	0.117144i
$918$	−8.85134	+	2.59899i	−0.292138	+	0.0857794i
$919$	6.75276			0.222753			0.111377	−	0.993778i	$-0.464474\pi$
$919$	6.75276			0.222753			0.111377	+	0.993778i	$0.464474\pi$
$920$	−0.829805	+	0.711919i	−0.0273579	+	0.0234713i
$921$	−20.1047			−0.662471
$922$	−73.7124	+	21.6439i	−2.42759	+	0.712804i
$923$	−2.09623	−	2.41918i	−0.0689984	−	0.0796284i
$924$	8.58986	−	5.52037i	0.282586	−	0.181607i
$925$	0.914411	+	6.35987i	0.0300656	+	0.209111i
$926$	18.0169	+	11.5787i	0.592071	+	0.380501i
$927$	4.50444	−	9.86335i	0.147945	−	0.323955i
$928$	40.1514	−	46.3372i	1.31803	−	1.52109i
$929$	6.07703	−	42.2667i	0.199381	−	1.38673i	−0.606705	−	0.794927i	$-0.707509\pi$
$929$	6.07703	−	42.2667i	0.199381	−	1.38673i	0.806086	−	0.591798i	$-0.201582\pi$
$930$	−14.8089	−	32.4269i	−0.485602	−	1.06332i
$931$	21.1334	+	6.20534i	0.692620	+	0.203372i
$932$	31.4240	+	9.22691i	1.02933	+	0.302238i
$933$	−7.09610	−	15.5383i	−0.232316	−	0.508701i
$934$	−4.22727	+	29.4013i	−0.138320	+	0.962040i
$935$	−10.1253	+	11.6852i	−0.331131	+	0.382146i
$936$	0.120033	−	0.262837i	0.00392342	−	0.00859108i
$937$	6.25612	+	4.02056i	0.204378	+	0.131346i	0.638826	−	0.769351i	$-0.279420\pi$
$937$	6.25612	+	4.02056i	0.204378	+	0.131346i	−0.434448	+	0.900697i	$0.643057\pi$
$938$	−3.40652	−	23.6928i	−0.111227	−	0.773599i
$939$	8.95065	−	5.75223i	0.292093	−	0.187717i
$940$	22.6817	+	26.1760i	0.739794	+	0.853768i
$941$	−44.5812	+	13.0902i	−1.45330	+	0.426729i	−0.910633	−	0.413216i	$-0.864405\pi$
$941$	−44.5812	+	13.0902i	−1.45330	+	0.426729i	−0.542672	+	0.839945i	$0.682587\pi$
$942$	−30.9938			−1.00983
$943$	13.5834	+	2.02121i	0.442338	+	0.0658196i
$944$	−20.6500			−0.672101
$945$	−6.35005	+	1.86454i	−0.206567	+	0.0606536i
$946$	7.88014	+	9.09417i	0.256206	+	0.295677i
$947$	−9.34041	+	6.00272i	−0.303522	+	0.195062i	−0.683532	−	0.729921i	$-0.739557\pi$
$947$	−9.34041	+	6.00272i	−0.303522	+	0.195062i	0.380010	+	0.924983i	$0.375921\pi$
$948$	−2.48654	−	17.2943i	−0.0807591	−	0.561692i
$949$	−25.7896	−	16.5740i	−0.837166	−	0.538014i
$950$	4.25355	−	9.31398i	0.138003	−	0.302185i
$951$	−10.3301	+	11.9216i	−0.334977	+	0.386585i
$952$	0.237829	−	1.65414i	0.00770810	−	0.0536110i
$953$	9.39201	+	20.5656i	0.304237	+	0.666187i	0.998570	−	0.0534679i	$-0.0170275\pi$
$953$	9.39201	+	20.5656i	0.304237	+	0.666187i	−0.694332	+	0.719654i	$0.744300\pi$
$954$	2.86483	+	0.841190i	0.0927522	+	0.0272345i
$955$	−6.34535	−	1.86316i	−0.205331	−	0.0602905i
$956$	11.5082	+	25.1995i	0.372203	+	0.815011i
$957$	−1.78676	+	12.4272i	−0.0577577	+	0.401713i
$958$	55.4394	−	63.9805i	1.79117	−	2.06712i
$959$	−6.00810	+	13.1559i	−0.194012	+	0.424827i
$960$	−12.9993	−	8.35413i	−0.419550	−	0.269628i
$961$	−6.52238	−	45.3641i	−0.210399	−	1.46336i
$962$	−34.5632	+	22.2124i	−1.11436	+	0.716156i
$963$	−3.00774	−	3.47111i	−0.0969230	−	0.111855i
$964$	−50.1719	+	14.7318i	−1.61593	+	0.474479i
$965$	8.94762			0.288034
$966$	−8.52621	−	29.5747i	−0.274326	−	0.951549i
$967$	0.0544688			0.00175160			0.000875800	−	1.00000i	$-0.499721\pi$
$967$	0.0544688			0.00175160			0.000875800		1.00000i	$0.499721\pi$
$968$	−0.892775	+	0.262142i	−0.0286949	+	0.00842558i
$969$	19.4559	+	22.4533i	0.625013	+	0.721303i
$970$	4.15649	−	2.67122i	0.133457	−	0.0857676i
$971$	6.92603	+	48.1716i	0.222267	+	1.54590i	0.729433	+	0.684052i	$0.239784\pi$
$971$	6.92603	+	48.1716i	0.222267	+	1.54590i	−0.507166	+	0.861848i	$0.669307\pi$
$972$	1.63535	+	1.05098i	0.0524539	+	0.0337101i
$973$	7.80785	−	17.0968i	0.250308	−	0.548098i
$974$	42.9164	−	49.5282i	1.37513	−	1.58699i
$975$	−0.297775	+	2.07107i	−0.00953643	+	0.0663273i
$976$	14.4394	+	31.6178i	0.462193	+	1.01206i
$977$	−52.8998	−	15.5328i	−1.69241	−	0.496938i	−0.713404	−	0.700753i	$-0.752848\pi$
$977$	−52.8998	−	15.5328i	−1.69241	−	0.496938i	−0.979009	+	0.203815i	$0.934666\pi$
$978$	−26.3438	−	7.73523i	−0.842381	−	0.247345i
$979$	−1.76372	−	3.86201i	−0.0563687	−	0.123430i
$980$	−1.95106	+	13.5699i	−0.0623242	+	0.433474i
$981$	−0.552902	+	0.638083i	−0.0176528	+	0.0203724i
$982$	25.1410	−	55.0510i	0.802280	−	1.75675i
$983$	−40.3538	−	25.9338i	−1.28709	−	0.827160i	−0.295341	−	0.955392i	$-0.595433\pi$
$983$	−40.3538	−	25.9338i	−1.28709	−	0.827160i	−0.991744	+	0.128232i	$0.959070\pi$
$984$	−0.0453667	−	0.315533i	−0.00144624	−	0.0100588i
$985$	−36.9985	+	23.7775i	−1.17887	+	0.757614i
$986$	−46.6642	−	53.8533i	−1.48609	−	1.71504i
$987$	26.9776	−	7.92135i	0.858708	−	0.252139i
$988$	32.2714			1.02669
$989$	16.2993	−	7.34704i	0.518289	−	0.233622i
$990$	6.61029			0.210089
$991$	25.2051	−	7.40089i	0.800667	−	0.235097i	0.144295	−	0.989535i	$-0.453908\pi$
$991$	25.2051	−	7.40089i	0.800667	−	0.235097i	0.656372	+	0.754438i	$0.272090\pi$
$992$	−45.5617	−	52.5810i	−1.44659	−	1.66945i
$993$	−10.3717	+	6.66549i	−0.329136	+	0.211523i
$994$	1.12642	+	7.83442i	0.0357279	+	0.248493i
$995$	10.9304	+	7.02452i	0.346516	+	0.222692i
$996$	−12.3845	+	27.1182i	−0.392417	+	0.859274i
$997$	−15.6901	+	18.1074i	−0.496912	+	0.573467i	−0.947699	−	0.319164i	$-0.896598\pi$
$997$	−15.6901	+	18.1074i	−0.496912	+	0.573467i	0.450787	+	0.892631i	$0.351143\pi$
$998$	7.55728	−	52.5621i	0.239222	−	1.66382i
$999$	3.31108	+	7.25025i	0.104758	+	0.229388i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.2.e.c.55.1	✓	20
3.2	odd	2		207.2.i.d.55.2		20
23.8	even	11		1587.2.a.u.1.9		10
23.15	odd	22		1587.2.a.t.1.9		10
23.18	even	11	inner	69.2.e.c.64.1	yes	20
69.8	odd	22		4761.2.a.bt.1.2		10
69.38	even	22		4761.2.a.bu.1.2		10
69.41	odd	22		207.2.i.d.64.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.e.c.55.1	✓	20	1.1	even	1	trivial
69.2.e.c.64.1	yes	20	23.18	even	11	inner
207.2.i.d.55.2		20	3.2	odd	2
207.2.i.d.64.2		20	69.41	odd	22
1587.2.a.t.1.9		10	23.15	odd	22
1587.2.a.u.1.9		10	23.8	even	11
4761.2.a.bt.1.2		10	69.8	odd	22
4761.2.a.bu.1.2		10	69.38	even	22

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	69.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.90549 + 0.559503i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(1.63535 - 1.05098i) q^{4} +(-0.291446 - 2.02705i) q^{5} +(1.67068 + 1.07368i) q^{6} +(1.34249 - 2.93963i) q^{7} +(0.0729013 - 0.0841325i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(-1.90549 + 0.559503i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(1.63535 - 1.05098i) q^{4} +(-0.291446 - 2.02705i) q^{5} +(1.67068 + 1.07368i) q^{6} +(1.34249 - 2.93963i) q^{7} +(0.0729013 - 0.0841325i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(1.68949 + 3.69946i) q^{10} +(-1.55951 - 0.457915i) q^{11} +(-1.86520 - 0.547672i) q^{12} +(-1.07824 - 2.36102i) q^{13} +(-0.913363 + 6.35258i) q^{14} +(-1.34109 + 1.54770i) q^{15} +(-1.70693 + 3.73765i) q^{16} +(3.90777 + 2.51137i) q^{17} +(-0.282628 - 1.96572i) q^{18} +(-5.38056 + 3.45787i) q^{19} +(-2.60700 - 3.00863i) q^{20} +(-3.10077 + 0.910468i) q^{21} +3.22785 q^{22} +(1.37375 - 4.59487i) q^{23} -0.111323 q^{24} +(0.773474 - 0.227113i) q^{25} +(3.37558 + 3.89563i) q^{26} +(0.841254 - 0.540641i) q^{27} +(-0.894050 - 6.21825i) q^{28} +(6.49822 + 4.17615i) q^{29} +(1.68949 - 3.69946i) q^{30} +(5.74006 - 6.62438i) q^{31} +(1.12962 - 7.85671i) q^{32} +(0.675196 + 1.47847i) q^{33} +(-8.85134 - 2.59899i) q^{34} +(-6.35005 - 1.86454i) q^{35} +(0.807544 + 1.76827i) q^{36} +(-1.13432 + 7.88940i) q^{37} +(8.31792 - 9.59939i) q^{38} +(-1.07824 + 2.36102i) q^{39} +(-0.191788 - 0.123254i) q^{40} +(0.407522 + 2.83438i) q^{41} +(5.39908 - 3.46978i) q^{42} +(2.44130 + 2.81741i) q^{43} +(-3.03161 + 0.890161i) q^{44} +2.04789 q^{45} +(-0.0468192 + 9.52410i) q^{46} -8.70030 q^{47} +(3.94253 - 1.15763i) q^{48} +(-2.25516 - 2.60259i) q^{49} +(-1.34678 + 0.865522i) q^{50} +(-0.661077 - 4.59789i) q^{51} +(-4.24468 - 2.72789i) q^{52} +(-0.624559 + 1.36759i) q^{53} +(-1.30051 + 1.50087i) q^{54} +(-0.473702 + 3.29467i) q^{55} +(-0.149450 - 0.327250i) q^{56} +(6.13680 + 1.80193i) q^{57} +(-14.7189 - 4.32185i) q^{58} +(2.08771 + 4.57145i) q^{59} +(-0.566554 + 3.94047i) q^{60} +(5.53965 - 6.39309i) q^{61} +(-7.23127 + 15.8343i) q^{62} +(2.71866 + 1.74718i) q^{63} +(1.07383 + 7.46864i) q^{64} +(-4.47166 + 2.87376i) q^{65} +(-2.11379 - 2.43945i) q^{66} +(-3.57857 + 1.05076i) q^{67} +9.02995 q^{68} +(-4.37218 + 1.97079i) q^{69} +13.1432 q^{70} +(1.18331 - 0.347451i) q^{71} +(0.0729013 + 0.0841325i) q^{72} +(9.93598 - 6.38547i) q^{73} +(-2.25270 - 15.6679i) q^{74} +(-0.678158 - 0.435826i) q^{75} +(-5.16495 + 11.3097i) q^{76} +(-3.43973 + 3.96966i) q^{77} +(0.733583 - 5.10218i) q^{78} +(3.73374 + 8.17574i) q^{79} +(8.07388 + 2.37071i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-2.36238 - 5.17288i) q^{82} +(2.18254 - 15.1799i) q^{83} +(-4.11396 + 4.74777i) q^{84} +(3.95177 - 8.65317i) q^{85} +(-6.22822 - 4.00264i) q^{86} +(-1.09930 - 7.64583i) q^{87} +(-0.152216 + 0.0978234i) q^{88} +(1.71060 + 1.97414i) q^{89} +(-3.90225 + 1.14580i) q^{90} -8.38806 q^{91} +(-2.58254 - 8.95799i) q^{92} -8.76531 q^{93} +(16.5784 - 4.86785i) q^{94} +(8.57742 + 9.89887i) q^{95} +(-6.67746 + 4.29134i) q^{96} +(-0.172893 - 1.20250i) q^{97} +(5.75334 + 3.69745i) q^{98} +(0.675196 - 1.47847i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 + 7 * q^6 - 6 * q^7 + 10 * q^8 - 2 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9} - 18 q^{10} - 16 q^{11} - 6 q^{12} + 14 q^{13} - 22 q^{14} + 5 q^{15} - 8 q^{16} + 11 q^{17} - 4 q^{18} - 11 q^{19} + 57 q^{20} - 6 q^{21} + 26 q^{22} - 12 q^{24} - 4 q^{25} - 14 q^{26} - 2 q^{27} - 14 q^{28} + 12 q^{29} - 18 q^{30} + 41 q^{31} - 46 q^{32} - 5 q^{33} - 3 q^{34} - 26 q^{35} + 5 q^{36} - 18 q^{37} + 70 q^{38} + 14 q^{39} - 13 q^{40} + 44 q^{42} - 10 q^{43} - 3 q^{44} + 16 q^{45} - 24 q^{46} + 18 q^{47} + 25 q^{48} - 10 q^{49} + 33 q^{50} + 61 q^{52} - 20 q^{53} + 7 q^{54} - 17 q^{55} + 6 q^{56} + 11 q^{57} - 37 q^{58} + 40 q^{59} - 31 q^{60} - 12 q^{61} - 89 q^{62} - 6 q^{63} - 2 q^{64} - 51 q^{65} + 15 q^{66} - 47 q^{67} - 12 q^{68} - 22 q^{69} + 32 q^{70} - 47 q^{71} + 10 q^{72} + 39 q^{73} - 50 q^{74} - 26 q^{75} - 39 q^{76} + 22 q^{77} - 14 q^{78} - 2 q^{79} + 12 q^{80} - 2 q^{81} + 26 q^{82} - 52 q^{83} - 14 q^{84} + 35 q^{85} + 34 q^{86} - 32 q^{87} + 30 q^{88} + 36 q^{89} - 18 q^{90} + 8 q^{91} - 19 q^{92} - 14 q^{93} + 21 q^{94} + 89 q^{95} - 2 q^{96} + 85 q^{98} - 5 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 + 7 * q^6 - 6 * q^7 + 10 * q^8 - 2 * q^9 - 18 * q^10 - 16 * q^11 - 6 * q^12 + 14 * q^13 - 22 * q^14 + 5 * q^15 - 8 * q^16 + 11 * q^17 - 4 * q^18 - 11 * q^19 + 57 * q^20 - 6 * q^21 + 26 * q^22 - 12 * q^24 - 4 * q^25 - 14 * q^26 - 2 * q^27 - 14 * q^28 + 12 * q^29 - 18 * q^30 + 41 * q^31 - 46 * q^32 - 5 * q^33 - 3 * q^34 - 26 * q^35 + 5 * q^36 - 18 * q^37 + 70 * q^38 + 14 * q^39 - 13 * q^40 + 44 * q^42 - 10 * q^43 - 3 * q^44 + 16 * q^45 - 24 * q^46 + 18 * q^47 + 25 * q^48 - 10 * q^49 + 33 * q^50 + 61 * q^52 - 20 * q^53 + 7 * q^54 - 17 * q^55 + 6 * q^56 + 11 * q^57 - 37 * q^58 + 40 * q^59 - 31 * q^60 - 12 * q^61 - 89 * q^62 - 6 * q^63 - 2 * q^64 - 51 * q^65 + 15 * q^66 - 47 * q^67 - 12 * q^68 - 22 * q^69 + 32 * q^70 - 47 * q^71 + 10 * q^72 + 39 * q^73 - 50 * q^74 - 26 * q^75 - 39 * q^76 + 22 * q^77 - 14 * q^78 - 2 * q^79 + 12 * q^80 - 2 * q^81 + 26 * q^82 - 52 * q^83 - 14 * q^84 + 35 * q^85 + 34 * q^86 - 32 * q^87 + 30 * q^88 + 36 * q^89 - 18 * q^90 + 8 * q^91 - 19 * q^92 - 14 * q^93 + 21 * q^94 + 89 * q^95 - 2 * q^96 + 85 * q^98 - 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more